LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

RECEIVED    BY  EXCHANGE 


Class 


THE 


HEAT  ENGINE  PROBLEM 


CHARLES  EDWARD   LUCRE,   M.S. 


SUK.MITTKD  IN  PARTIAL  FULFILMENT  OF  THE  REQUIREMENTS  FOR  THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  THE 
FACULTY  OF  APPLIED  SCIENCE,  COLUMBIA  UNIVERSITY. 


NEW    YORK 
1902 


THE 


HEAT  ENGINE  PROBLEM 


BY 


CHARLES  EDWARD   LUCKE,   M.S. 


SUBMITTED  IN  PARTIAL  FULFILMENT  OF  THE  REQUIREMENTS  FOR  THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  THE 
FACULTY  OF  APPLIED  SCIENCE,  COLUMBIA  UNIVERSITY. 


t      / 


NEW    YORK 
1902 


V 


' 


CONTENTS. 


PAGE. 

THE  HEAT  ENGINE  PROBLEM      .......      i 

Introduction        .........      i 

Resume  of  Work  and  Results         .          .          ....     3 

A  METHOD  OF  CYCLIC  ANALYSIS  OF  HEAT  ENGINES    .         .  9 

Heat  Engine  Cycles  Analyzed       .          .          .          ...     9 

The  Atmospheric  or  Vacuum  Cycles       .          .          .          .  I9 

Comparison  of  Cycles  .          .          .          .          .          .  .   82 

k  Temperatures  after  Addition  of  Hv  B.  T.  U.          .          .   82 

Pressures  after  Addition  of  #j,  B.  T.  U.          .          .          .84 

Volumes  after  Heating  by  ffv  B.  T.  U.          .          .          .85 

Temperature  after  Expansion  .          .          .          .          .86 

Pressures  after  Expansion       .          .          .          .          .          .87 

Volumes  after  Expansion       .          .          .          .          .          .89 

Heat  Discharged  or  Abstracted       .          .          .          .          .90 

General  Propositions     .          .          .          .          .          .          .94 

Efficiencies  ........   05 

Temperatures        ........    96 

Pressures      .          .          .          .          .          .          .          .          .08 

Volumes       .          .          .          .  .          .          .          .    99 

THE  HEAT  ENGINE  PROBLEM  (No.  926)      .         .         .  .  l 

Coal -burning  Engines  ......  .20 

Oil-burning  Engines    .          .          .          .          .          .  .  .29 

Gas-burning  Engines    .          .          .          .          .          .  .  ^r 

LIQUID  FUEL  COMBUSTION  (No.  0934)  .         .         .         .  I 

PHYSICAL  PROPERTIES  OF  EXPLOSIVE  MIXTURES      .         .         .         .  i 

Rate  of  Propagation     ........  5 

Temperature  of  Combustion           ......  7 

Resume  of  Temperature  of  Combustion           .          .  8 


218506 


2  CONTENTS. 

PAGE. 

SOME  NEW  WORK  ON  PROPERTIES  OF  EXPLOSIVE  MIXTURES      .  .12 

The  Apparatus     .......  .12 

Neutral  Gas  Generator          .....  .15 

Constant  Pressure  Combustion  Gas  Calorimeter       .          .  .16 

Constant  Volume  Combustion  Pressure  Ratio  Chamber   .  .17 

Constant  Pressure  Combustion  Volume  Ratio  Apparatus  .  .18 

Results  Obtained  with  Apparatus.     P'lames  in  Atmosphere  of 

Different  Air-Gas  Mixtures          .       .  »         .          .  .20 

Constant  Pressure  Combustion  Calorimeter      .          .  .22 

Volume-ratios  During  Constant  Pressure  Combustion  .    26 

Pressure-ratios  for  Constant  Volume  Combustion      .  .27 

Conclusion           .          .          .          .          .          .          .         •»  -3° 


THE    HEAT    ENGINE    PROBLEM. 

INTRODUCTION. 

IT  is  now  a  good  many  years  since  the  first  proposition  was 
made  for  obtaining  work  by  the  heat-transforming  action  of  a  per- 
fect gas  and  though  each  process  as  it  appeared  has  been  more  or 
less  completely  worked  out  by  those  interested  in  it  to  show  the 
possibilities  of  the  system  and  compare  it  with  others  yet  no  inves- 
tigation of  all  systems  with  their  mutual  relations  has  ever  been 
made  by  a  general  method.  This  is  desirable  because  no  compari- 
sons can  be  justly  drawn  otherwise  and  it  is,  unfortunately,  true 
that  invariably  in  the  past  the  best  conditions  of  one  system  have 
beenv  selected  for  comparison  with  some  other  system  working 
under  indifferent  conditions.  This  may  not  have  been  done  inten- 
tionally, in  fact  it  appears  that  in  many  cases  the  comparison 
seemed  perfectly  just  to  the  author  but  the  results  are  almost 
valueless  as  bases  of  generalization  for  the  purpose  of  reaching 
clear  notions  of  comparative  value. 

A  commonly  used  mode  of  comparison  considers  different  cycles 
working  through  the  same  temperature  range  whereas  equal  quanti- 
ties of  heat  for  each  case  will  result  in  different  temperature  ranges 
and  it  is  pretty  clear  that  comparisons  should  be  made  on  the  basis 
of  some  initial  conditions  one  of  which  is  the  heat  supplied. 

A  perfect  gas  will  transform  heat  into  work  and  considering  the 
gas  alone  without  reference  to  any  engine  the  fraction  of  the  heat 
that  is  transformed  is  dependent  on  the  relation  both  in  sequence 
and  extent  of  the  operations  of  heating,  cooling,  expansion  and 
contraction — in  short  is  dependent  on  the  cycle  first  and  the  extent 
of  each  cyclic  phase  secondly.  It  is  first  required  to  find  out  just 
how  much  heat  energy  will  be  transformed  by  each  cycle  and  if 
other  things  are  equal  one  should  be  the  best  for  application  to 
engines.  But  in  this  comparison  we  should  consider  not  only 
which  cycle  transforms  the  largest  amount  of  the  heat  energy 
supplied  to  it  into  work  but  also  through  just  what  range  of  pres- 
sures, volumes  and  temperatures  these  cycles  must  operate  to 
produce  the  work  This  comparison  will  be  purely  mathematical 
and  will,  when  completed,  enable  us  to  select  the  best  cycle  or  best 
two  cycles  as  the  case  may  be,  i.  e.,  that  one  or  those  two  cycles 

i 


2  ...  9.  t..Ttq:..yEAT    ENGINE    PROBLEM. 

that  promise  the  best  returns  for  the  labor  spent  on  designing 
mechanism  to  execute  the  cyclic  changes. 

Having  made  the  mathematical  selection  of  the  cycles  best 
adapted  to  our  purpose  we  are  called  upon  to  consider  how  to 
heat  or  cool  to  cause  expansion  or  contraction  with  the  means  at 
our  command  and  at  the  rate  required.  This  second  part  involves 
all  questions  of  possibility  or  practicability  of  doing  what  seemed 
mathematically  to  be  desirable. 

To  place  each  of  the  cycles  in  proper  relation  each  with  the  other 
and  to  show  the  physical  possibility  of  executing  those  promising 
good  returns  as  power  generators  is  the  general  problem.  More 
particularly  the  question  resolves  itself  into  a  search  for  an  effec- 
tive competitor  of  the  Otto  cycle  engine  which  now  is  the  only 
good  heat  engine  of  the  perfect  gas  sort. 

As  the  work  progressed  beyond  the  mathematical  analytic  stage 
there  appeared  a  cycle  which  promised  good  returns  for  any  labor 
expended  on  its  development  but  which  has  been  comparatively 
neglected.  The  latter  part  of  the  work  is  taken  up  with  a  study 
of  physical  and  engineering  problems  entering  into  the  execution 
of  this  theoretically  desirable  cycle  in  engines  and  includes  the 
determination  of  many  of  the  physical  constants  necessary  for 
computation  of  designs.  In  this  part  also  there  is  set  down  all 
the  difficulties  to  be  encountered  and  both  the  solutions  obtained 
and  the  need  of  solutions  for  those  questions  still  open  are  noted. 


RESUME  OF  WORK  AND  RESULTS. 

The  work  was   taken  up  in  detail  as  follows,  and  each  section 
brought  to  a  successful  conclusion  except  where  otherwise  stated  : 

PART    I. 

NEW  CLASSIFICATION  OF  CYCLES  AND    DIAGRAMS  OF  SAME  IN 

P.  V.  &  6$  COORDINATES. 

Cycle  I     Isometric  heating;  adiabatic  expansion;  isopiestic  cooling. 
Cycle  IA  Isometric  heating  ;  adiabatic  expansion  ;  isometric  cool- 
ing ;  isopiestic  cooling. 

Cycle  IB  Isometric  heating  ;  adiabatic  expansion  ;  isothermal  cool- 
ing ;  isopiestic  cooling. 
Cycle  1C  Isometric    heating ;    adiabatic     expansion ;    isothermal 

cooling. 
Cycle  II         Adiabatic  compression  ;  isometric  heating ;  adiabatic 

expansion  ;  isopiestic  cooling. 
Cycle  IIA2    Adiabatic  compression  ;  isometric  heating ;  adiabatic 

expansion  ;  isometric  cooling. 
Cycle  UAl    Adiabatic  compression  ;  isometric  heating  ;    adiabatic 

expansion  ;  isometric  cooling  ;  isopiestic  cooling. 
Cycle  IIB     Adiabatic  compression;   isometric  heating ;  adiabatic 

expansion  ;  isothermal  cooling ;   isopiestic  cooling. 
Cycle  IIC     Adiabatic  compression  ;  isometric  heating;  adiabatic 

expansion  ;  isothermal  cooling. 
Cycle  III       Adiabatic  compression  ;  isopiestic  heating ;  adiabatic 

expansion  ;  isopiestic    cooling. 
Cycle  IIIA  Adiabatic  compression  ;  isopiestic  heating ;  adiabatic 

expansion  ;  isometric  cooling  ;  isopiestic  cooling. 
Cycle  IIIB  Adiabatic  compression  ;  isopiestic  heating ;  adiabatic 
^expansion;  isothermal  cooling;  isopiestic  cooling. 
Cycle  1 1 1C  Adiabatic  compression  ;  isopiestic  heating  ;  adiabatic 

expansion  ;  isothermal    cooling. 
Cycle  IV      Adiabatic  compression  ;  isothermal  heating  ;  adiabatic 

expansion  ;  isopiestic  cooling. 
Cycle  IVA  Adiabatic  compression  ;  isothermal  heating  ;  adiabatic 

expansion  ;  isometric  cooling  ;  isopiestic  cooling. 
Cycle  IVB  Adiabatic  compression  ;  isothermal  heating  ;  adiabatic 

expansion  ;  isothermal  cooling  ;  isopiestic  cooling. 

3 


4  THE  HEAT  ENGINE  PROBLEM. 

Cycle  IVC  Adiabatic  compression  ;  isothermal  heating  ;  adiabatic 

expansion  ;  isothermal  cooling. 
Cycle  V       Adiabatic  compression  ;   any  law  of  heating  ;   adiabatic 

expansion  ;  isopiestic  cooling. 


VB   >  Similar  meanings  to  preceding  cases. 

vcj 

Cycle  VI       Atmospheric  heating  ;    isometric  cooling  ;  isothermal 

cooling. 
Cycle  VII     Atmospheric  heating  ;  adiabatic  expansion  ;  isopiestic 

cooling  ;  adiabatic  compression. 
Cycle  VIII  Atmospheric  heating  ;  adiabatic  expansion  ;  isothermal 

cooling. 
Cycle  IX       Atmospheric  heating  ;  adiabatic  expansion  ;  isometric 

cooling  ;  adiabatic  compression. 
Cycle  X        Atmospheric  heating  ;  adiabatic  expansion  ;  any  law 

of   cooling  ;    adiabatic  compression. 

FOR   EACH   CYCLE  A   FORMULA   is   DERIVED    EXPRESSING    EACH 
OF  THE  FOLLOWING  VARIABLES  AS  A  FUNCTION 

OF  THE  HEAT  SUPPLIED  Hv 
(py  v,  T)  for  every  point  of  the  diagram. 
7/2  or  the  heat  discharged  as  unavailable. 
W  —  Hl  —  H2  or  the  amount  of  energy  transformed  into  work. 

TT 

E—I—~    or  the  efficiency,  the  fraction   of  energy  supplied 

"\ 
that  becomes  transformed  to  work. 

R^  or  entropy  range. 

(TT        ,         TT     \ 
—  l—  —  -2-  ]  or  mean  -effective  temperature. 
K(f      ) 

Rv  or  volume  range. 

M.E.P.  =  ~r  or  mean-effective  pressure. 

R, 
Rn  or  pressure  range. 

M.E.V.  —  -=r-0r  mean  effective  volume. 

RP 
R(  or  temperature  range. 

CYCLES  COMPARED. 

The  formulae  derived  are  here  collected  and  curves  drawn  in 
two  coordinates.     One  coordinate  is  in  every  case  //,  the  heat  sup- 


R£SUM£.  5 

plied  and  the  other  coordinate  the  variable  under  consideration. 
This  gives  one  curve  in  every  set  for  each  cycle  and  as  many  sets 
as  there  are  variables.  Some  of  these  are  less  important  than 
others  and  the  former  are  omitted  and  a  set  presented  for  each  of 
the  following. 

Curves  of  Temperature  after  Heating. 

Curves  of  Pressure  "  " 

Curves  of  Volume  "  " 

Curves  of  Temperature  after  Expansion. 

Curves  of  Pressure  "  " 

Curves  of  Volumes  "  " 

Curves  of  Heat  Discharged  or  Abstracted. 

Curves  of  Efficiency. 

Curves  of  Mean  Effective  Pressure. 

Curves  of  Mean  Effective  Volume. 

Curves  of  Mean  Effective  Temperature. 

Comparison  and  interpretation  of  curves. 

Selection  of  a  cycle  to  be  applied  to  engines,  the  selection  based 
on  theoretic  grounds  alone. 

PART  II. 
THE  EXECUTION  OF  THE  CYCLES  BY  MECHANISMS. 

All  heat  to  be  derived  from  a  fire  and  may  be  imparted  to  the 
gas  in  three  ways  :  (a)  Through  walls,  (fr)  by  introduction  of 
hot  body,  (c)  internal  combustion. 

External  heating  condemned. 

Introduction  of  hot  masses  impracticable. 

Internal  combustion  advocated. 

Internal  heating  by  coal,  oil,  gas. 

Explosive  internal  combustion. 

Non-explosive  internal  combustion. 

Explosive  internal  combustion  in  engines  discussed. 

Explosive  engines  pretty  well  known  and  now  receiving  much 
attention  hence  this  question  left  for  study  of  less  well  known  types. 

Other  types  of  internal  combustion  engine  considered  alone  and 
in  relation  to  others. 

Two  typical  classes  of  these  non-explosive  engines  stand  far  in 
front  of  others  from  every  point  of  view,  the  Brayton  and  the  Diesel. 

Review  of  cyclic  analysis  so  far  as  it  refers  to  the  three  typical 
cases  of  the  practicable  cycles. 


6  THE  HEAT  ENGINE  PROBLEM. 

Left  for  further  study  Diesel,  Otto,  Brayton  and  their  variations. 

Diesel  an  imperfect  Carnot  and  from  analysis  may  be  neglected 
in  comparison  with  the  Brayton  for  power  generation. 

This  leaves  as  the  cycle  worthy  of  application  but  little  known 
and  not  at  all  recognized,  Brayton's  with  its  variations. 

Special  problems  introduced  by  the  internal-combustion  method 
of  heating,  (a)  What  specific  heat  is  to  be  used  in  calculating 
rise  of  temperature  during  a  chemical  change,  that  of  the  constitu- 
ents, that  of  the  products,  or  something  different  from  both,  (b) 
Volume  change  due  to  chemical  action,  (c)  Is  the  heat  of  com- 
bustion of  a  mass  of  fuel  constant  or  does  this  depend  on  conditions, 
and  if  so  determine  them. 

Heat  suppression  in  combustion  as  evidenced  by  the  discrepancy 

i)  i) 
between  observed  —  and  —  and  theoretic  values  of  the  same  for 

A  "i 
the  isometric  and  isopiestic  combustion  respectively. 

Effective  specific  heat  versus  effective  calorific  power. 

A  variation  of  calorific  value  with  the  method  of  combustion 
would  give  Otto  or  Brayton  the  preference  in  efficiency  as  the  case 
might  be. 

The  non-explosive,  internal  combustion  engine  has  three  ele- 
ments, fuel  and  air  supply,  fire-box,  expansion  parts. 

Fuel  and  air  supply  require  no  study  as  pumps  and  compressors 
are  well-known  machines. 

Utilization  of  hot  expanding  gases  in  cylinders  and  turbines  has 
been  done  and  requires  only  enough  study  to  reduce  to  good 
practice  ;  there  is  nothing  of  the  impossible. 

The  combustion  phase  is  where  the  trouble  has  been,  no  entirely 
successful  fire-box  has  yet  been  proposed  that  will  meet  all  require- 
ments though  some  there  are  that  work  very  well  under  specified 
conditions. 

The  engines  of  this  class  would  have  great  elasticity  of  action 
in  speed,  power  and  direction  of  motion,  they  would  be  able  to  pull 
up  to  an  overload  and  they  can  be  constructed  to  burn  any  fuel. 

Coal-burning  engines  build  and  proposed,  typical  cuts. 

Oil-burning  engines  built  and  proposed,  typical  cuts. 

Gas-burning  engines  built  and  proposed,  typical  cuts. 

Details  of  Construction  Compared. — Cylinders,  igniters,  gover- 
nors, preheaters,  regenerators,  fuel  feeds,  gas  burners,  oil  burners, 
mixers,  proportioners,  use  of  water,  position  of  fire. 


RESUME.  7 

All  cycles  possible  with  the  non-explosive  internal  combustion 
engine. 

The  engine  built  by  George  Bray  ton,  its  abandonment  and 
eclipse  by  the  Otto  machine. 

Only  non-explosive  internal-combustion  engine  working  to-day 
is  that  of  Diesel. 

The  Diesel  engine  in  practice  working  not  under  the  modified 
Carnot  cycle  but  under  the  Brayton  cycle.  It  is  then  rather  a 
modified  Brayton. 

The  cause  of  failure  in  other  attempts  at  application  of  Brayton 
or  modified  Brayton  cycles  invariably  traceable  to  the  fire-box  or 
method  of  combustion,  therefore  investigation  of  methods  of  burn- 
ing oil  and  gas  necessary. 

Methods  of  gas  combustion  classified. 

Combustion  of  gases  and  mixtures  requiring  an  atmosphere  and 
producing  a  volume  of  flame. 

Combustion  of  explosive  mixtures  by  self  propagation  :  (a)  at 
rest  and  (b)  in  motion. 

Requirements  of  proper  method  for  the  combustion  of  explosive 
mixtures  in  motion. 

Experiments  made  in  search  for  means  to  fulfill  the  require- 
ments. 

New  method  of  combustion  of  explosive  mixtures  in  motion  a 
close  approach  to  ideal. 

The  explosive  gas  fire. 

Operation  of  the  internal  combustion  engine  by  intermittent  com- 
bustion in  which  the  mixture  leaves  after  passing  the  inlet  valve  to 
expansion  space. 

Operation  of  engines  with  continuous  combustion,  the  fire  burn- 
ing steadily  and  the  inlet  valves  controlling  the  burnt  hot  gases. 

PART  III. 

LIQUID  FUEL  COMBUSTION. 

Oil  combustion,  a  series  of  physical  actions  involving  a  knowl- 
edge of  gas  combustion  and  to  be  studied  in  the  light  of  that 
knowledge. 

Different  oil  systems  differ,  (a)  in  the  method  of  producing  the 
vapor  or  oil -gas,  and  (ti)  in  the  methods  of  causing  a  meeting  of 
this  vapor  with  the  air. 

Oil  combustion  classified. 


8  THE  HEAT  ENGINE  PROBLEM. 

Historical  review  of  different  classes  by  studying  characteristic 
systems. 

Requirements  for  enclosed  pressure  system  to  be  used  in  the 
internal-combustion  engine. 

Report  of  series  of  experiments  having  for  their  aim  the  dis- 
covery of  a  suitable  system. 

The  "  explosive  oil  fire,"  as  developed,  proves  satisfactory  and 
suitable. 

Some  experiments  and  notes  to  test  the  availability  of  the  "  ex- 
plosive oil  fire  "  for  other  uses. 

PART    IV. 
PHYSICAL  PROPERTIES  OF  EXPLOSIVE  MIXTURES. 

Historical  sketch  reviewing  present  knowledge  of  the  properties 
of  explosive  mixtures. 

No  data  sufficient  for  computation  of  many  of  the  quantities 
needed  in  the  application  of  explosive  mixtures  to  engineering  work. 

Object  of  this  part  not  only  to  discover  if  possible  a  properly 
simple  and  accurate  means  for  obtaining  such  data,  but  also  to  use 
the  apparatus  in  the  making  of  such  observations  as  time  might 
permit. 

Apparatus  designed  and  used  for  — 

fgas> 
i°  Measuring^  air, 

t  neutral  products  of  combustion. 
2°   Mixing,  compressing  and  storing  the  mixture. 
3°   Producing  products  of  combustion  by  method  available  for 
collection  and  storage. 

4°  Measuring  the  heat  of  combustion  of  explosive  mixtures 
directly  by  burning  at  constant  volume. 

5°  The  same  as  4°  but  by  burning  at  constant  pressure. 
6°   Measuring   pressures   due  to   constant  volume   combustion 
directly. 

7°  Measuring  volume's  increases  due  to  constant  pressure  com- 
bustion directly. 

PART    V. 

CONCLUSION. 

Review  of  work  done,  results  attained,  and  statement  of  what 
remains  to  be  done. 


A    METHOD    OF    CYCLIC    ANALYSIS    OF    HEAT 
ENGINES. 

HEAT  ENGINE  CYCLES  ANALYZED. 

Prime  movers  are  useful  when  they  produce  motion  in  required 
directions  against  resistances.  Nearly  all  our  machines  which  in 
general  constitute  the  resistance  to  prime  movers  are  designed  to 
be  operated  through  an  applied  forceful  rotary  motion  ;  therefore 
the  prune  movers  that  are  to  be  of  most  service  to  us  in  our  ordi- 
nary working  operations  must  develop  forced  rotary  motion.  By 
far  th'e  largest  number  of  these  rotary  motion  prime  movers  come 
under  the  head  of  Heat  Engines.  These  heat  engines  may  be 
divided  into  two  classes  : 

(a)  Those  that  do  work  by  utilizing  the  expansion  of  a  sub- 
stance when  changing  from  the  liquid  to  the  gaseous  state. 

(ft)  Those  that  do  work  by  utilizing  the  expansion  of  a  perfect 
gas,  this  expansion  being  caused  in  some  mysterious  way  by  ab- 
sorption of  heat. 

The  engines  of  class  a  usually  consist  of  two  parts,  a  part  for 
the  production  of  the  vapor,  and  a  part  for  the  utilization  of  this 
vapor,  converting  an  increase  of  volume  into  a  forced  rotary  motion, 
in  ordinary  language,  of  a  boiler  and  an  engine  proper.  The 
amount  of  work  that  can  be  done  with  a  given  amount  of  heat  by 
a  prime  mover  of  this  class,  is  definitely  known  within  certain 
limits,  when  we  know  how  much  liquid  can  be  converted  into 
vapor  by  this  heat,  and  the  relative  specific  volumes  of  the  liquid 
and  resulting  vapor.  It  therefore  depends  chiefly  on  the  liquid 
chosen,  and,  of  course,  on  the  mechanical  efficiency  of  the  system 
as  a  converter,  or,  as  we  may  say,  on  the  design  of  the  machine. 

The  cycle  of  operations  is  :  (I.)  Add  heat  to  liquid  and  pro- 
duce vapor.  (II.)  Allow  vapor  to  expand  to  as  low  a  pressure  as 
possible,  and  then  discharge  it  either  as  vapor  or  as  a  reconverted 
liquid. 

This  cycle  is  unchangeable  except  in  incidental  details.  On  the 
contrary,  however,  when  we  employ  a  perfect  gas  to  which  to 
apply  our  heat,  and  whose  expansion  gives  us  our  work,  we  may 
have  a  large  range  of  different  cycles  or  series  of  operations  that 

9 


10  THE    HEAT    ENGINE    PROBLEM. 

may  be  performed  on  or  by  the  gas  in  question.  The  amount  of 
work  done  by  our  expanding  gas  due  to  the  initial  application  of  a 
given  amount  of  heat  will  depend  on  the  manner  of  heating,  method 
of  expansion,  ultimate  disposition  of  the  gas,  and,  of  course,  on  the 
mechanical  efficiency  of  the  machine  for  performing  the  operations 
desired,  and  will  depend  not  at  all  on  the  gas  chosen.  In  short, 
the  varying  amounts  of  work  that  may  be  done  will  depend  solely 
on  the  cycle  itself.  It  is  therefore  evident  that  there  is  consider- 
able importance  in  knowing  just  how  the  cycle  can  effect  this 
change  of  ultimate  useful  work  for  given  heat  supplied. 

In  the  actual  application  of  any  cyclic  principles  we  find  various 
other  questions  beside  the  ultimate  useful  work  that  demand  at- 
tention and  study.  For  example,  one  cycle  requires  a  larger  vol- 
ume of  gas  to  do  same  work  as  another  ;  a  larger  engine  is  therefore 
necessary ;  some  cycles  operate  under  higher  temperatures  than 
others  ;  some  through  wider  ranges  of  temperature  and  pressure. 
Many  other  questions  might  be  cited,  but  enough  are  given  to  show 
that  it  is  necessary  that  we  study  the  cycles  as  such,  and  obtain  a 
statement  of  every  question  in  terms  of  the  cycle,  before  we  begin 
the  consideration  of  the  mechanical  difficulties  involved  in  its  car- 
rying out. 

It  is  possible  to  cause  a  similar  mass  of  perfect  gas  to  pass 
through  each  of  the  cycles,  and  obtain  an  equation  for  every  vari- 
able entering  into  the  cycle  in  terms  of  the  initial  conditions  and 
the  quantity  of  heat  supplied.  For  example,  we  can  write 

For  cycle      I.  Efficiency  =  £=/I(HlC') 
For  cycle    II.  E=fn(HlClt) 

For  cycle  III.  E=fm(H£'"} 

For  cycle;.,  E=fn(H,C")    ' 

where  H^  is  heat  supplied,  and  C  a  constant. 

We  thus  get  a  series  of  curves  of  efficiency,  one  for  each  cycle, 
in  terms  of  the  same  variable,  and  get  exact  relations  of  the  cycles 
regarding  efficiency  at  a  glance.  Instead  of  efficiency  we  might 
have  chosen  the  final  volumes  or  the  maximum  temperatures. 

It  is  the  object  of  this  part  to  consider  the  various  cycles  as 
above  outlined  and  cause  one  pound  of  air  to  pass  through  each 
of  the  cycles  under  ideal  conditions,  and  to. determine  every  cyclic 
variable  in  terms  of  Hv  and  arbitrary  initial  conditions.  To  pass 
from  ideal  conditions  to  practical  ones  we  need  only  apply  a  cor- 
rection factor. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


1 1 


In  what  follows  we  shall  not  consider  how  the  heat  is  applied 
or  abstracted,  the  mechanisms  involved,  nor  the  practicability  of 
the  process. 

The  following  cycles  will  be  considered : 

CYCLE.  I  e 


B 


FIG.  i. 


FIG.  2. 


Let  Fig.  i  be  a  P.V.  and  Tig.  2  be  a  O(p  diagram  for  the  cycle. 
Then  we  have  : 

From  B  to  C.     Addition  of  heat  isometric'ally  from  atmospheric 
pressure. 

From  C  to  D.  Adiabatic  expansion  to  atmospheric  pressure. 
From  D  to  B.   Cooling  at  atmospheric  pressure. 

P 


CYCLE  I -A. 


e. 


B 


E. 


FIG.  3.  FIG.  4. 

We  have : 

From  B  to  C.  Addition  of  heat  isometrically  from  atmospheric 
pressure. 

From  C  and  D.  Adiabatic  expansion  to  point  above  atmos- 
pheric pressure. 


12 


THE    HEAT    ENGINE    PROBLEM. 


From  D  and  E.   Cooling  isometrically  to  atmospheric  pressure. 
From  E  to  B.   Cooling  at  atmospheric  pressure. 


CYCLE  IB. 


P> 


FIG.  5.  FIG.  6. 

We  have  : 

From  B  to  C.  Addition  of  heat  isometrically  from  atmospheric 
pressure. 

From  C  to  D.  Adiabatic  expansion  to  below  atmospheric  pres- 
sure. 

From  D  to  E.  Cooling  isothermally  to  atmospheric  pressure. 

From  E  to  B.  Cooling  at  atmospheric  pressure. 


CYCLE  1C 


C.  ' 


B 


I). 


V 


FIG.  7.  FIG.  8. 

We  have  : 

From  B  to  C.  Addition  of  heat  isothermally  from  atmospheric 
pressure. 

From  C  to  D.  Adiabatic  expansion  to  pressure  below  atmos- 
phere such  that  we  get, 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


From  D  to  B.   Cooling  isothermal ly  to  original  volume  and  at 
mospheric  pressure. 


p 


CYCLE 


A. 


FIG.  9.  FIG.  10. 

We  have : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pressure. 
From  B  to  C.  Addition  of  heat  isometrically. 
From  C  to  D.  Adiabatic  expansion  to  atmospheric  pressure. 
From  D  to  A.  Cooling  at  atmospheric  pressure. 

CYCLE  HA.  @ 


V 
FIG.  ii.  FIG.  12. 

We  have : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pres- 
sure. 

From  B  to  C.  Addition  of  heat  isometrically. 

From  C  to  D.  Adiabatic  expansion  to  pressure  above  atmos- 
phere. 

From  D  to  E.  Cooling  isometrically  to  atmosphere. 

From  E  to  A,  Cooling  at  atmospheric  pressure. 


H 
P 


THE    HEAT    ENGINE    PROBLEM. 
CYCLE  JPB.  e 


B 


A.     E. 


C. 


E. 


D 


V 


FIG.  13. 


FIG.  14. 


We  have  : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pres- 
sure. 

From  B  to  C.  Addition  of  heat  isometrically. 

From  C  to  D.  Adiabatic  expansion  to  pressure  below  atmos- 
phere. 

From  D  to  E.  Cooling  isothermally  to  atmospheric  pressure. 

From  E  to  A.  Cooling  at  atmospheric  pressure. 


CYCLE  1IC 


B 


A. 


D. 


FIG.  15.  FIG.  1 6. 

We  have : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pressure. 

From  B  to  C.  Addition  of  heat  isometrically. 

From  C  to  D.  Adiabatic  expansion  to  pressure  below  atmos- 
phere such  that  we  get, 

From  D  to  A.  Cooling  isothermally  to  original  volume  and  -at- 
mospheric pressure. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 
CYCLE  111  @ 


FIG.   17. 


We  have  : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pressure. 

From  B  to  C.  Addition  of  heat  isopiestically. 

From  C  to  D.  Adiabatic  expansion  to  atmospheric  pressure. 

From  D  to  A.  Cooling  at  atmospheric  pressure. 


CYCLE  JIIA. 


FIG.  19. 


FIG.  20. 


We  have  : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pres- 
sure. 

From  B  to  C.  Addition  of  heat  isopiestically. 

From  C  to  D.  Adiabatic  expansion  to  pressure  above  atmos- 
phere. 

From   D  to  E.   Cooling  isometrically  to  atmospheric  pressure. 

From  E  to  A.   Cooling  at  atmospheric  pressure. 


i6 


THE    HEAT    ENGINE    PROBLEM. 
CYCLE    1HB 


'  A 


FIG.  21. 


FIG.  22. 


We  have  : 

From  A  to  B.  Adiobatic  compression  from  atmospheric  pressure. 

From  B  to  C.  Addition  of  heat  isopiestically. 

From  C  to  D.  Adiabatic  expansion  to  pressure  below  atmos- 
phere. 

From  D  to  E.  Cooling  isothermally  to  atmospheric  pressure. 

From  E  to  A.  Cooling  at  atmospheric  pressure. 

CYCLE  me. 


A. 


V  • 


I), 


FIG.  24. 


We  have  : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pres- 


sure. 


From  B  to  C.  Addition  of  heat  isopiestically. 

From  C  to  D.  Adiabatic  expansion  to  pressure  below  atmos- 
phere such  that  we  get, 

From  D  to  A.  Cooling  isothermally  to  original  volume  and  at- 
mospheric pressure. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 
P      B.  8. 


B 


FIG.  25.  FIG.  26. 

We  have  : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pressure. 
From  B  to  C.  Addition  of  heat  isothermally. 
From  C  to  D.  Adiabatic  expansion  to  atmospheric  pressure. 
From  E  to  A.  Cooling  at  atmospheric  pressure. 
P   IB.  CYCLE   IV A.  6- 


B 


E. 


FIG.  27.  FIG.  28. 

We  have  : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pressure. 
From  B  to  C.  Addition  of  heat  isothermally. 
From  C  to  D.  Adiabatic  expansion  to  pressure  above  atmos- 
phere. 

From  D  to  E.   Cooling  isometrically  to  atmospheric  pressure. 
From  E  to  A.   Cooling  at  atmospheric  pressure. 


THE    HEAT    ENGINE    PROBLEM. 
CYCLE   IVB 


B 


C. 


FIG.  29.  FIG.  30. 

We  have : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pressure. 
From  B  to  C,  Addition  of  heat  isothermally. 
From  C  to  D.  Adiabatic  expansion  to  pressure  below  atmosphere. 
From  D  to  E.  Cooling  isothermally  to  atmospheric  pressure. 
From  E  to  A.  Cooling  at  atmospheric  pressure. 
P     B  CYCLE  IVQ 


B 


A. 


D, 


FIG.  31. 


FIG.  32. 


We  have : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pressure. 

From  B  to  C.  Addition  of  heat  isothermally. 

From  C  to  D.  Adiabatic  expansion  to  pressure  below  atmos- 
phere such  that  we  get, 

From  D  to  A.  Cooling  isothermally  to  original  volume  and 
atmospheric  pressure. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 
CYCLE  V. 


FIG.  33. 


FIG.  34. 


We  have  : 

From  A  to  B.  Adiabatic  compression  from  atmospheric  pres- 
sure. 

From  B  to  C.     Addition  of  heat  at  variable  pvd. 

From  C  to  D.     Adiabatic  expansion  to  atmospheric  pressure. 

From  D  to  A.  Cooling  at  atmospheric  pressure. 

Cycles  V.,  A,  B  and  £7  may  have  the  same  modification  on  Cycle 
V.  as  II.  A,  B  and  C  have  on  III.,  for  example. 

THE  ATMOSPHERIC  OR  VACUUM  CYCLES. 

Here  all  the  cyclic  operations  take  place  at  or  below  atmos- 
pheric pressure. 


CYCLE  W. 


P 


0. 
A 


B. 


B, 


V 


FIG.  35. 


FIG.  36. 


We  have  : 

From  A  to  B.  Addition  of  heat  at  atmospheric  pressure. 

From  B  to  C.  Cooling  isometrically. 

From  C  to  A.  Adiabatic  compression. 


20 


THE    HEAT    ENGINE    PROBLEM. 
CYCLE    W. 


FIG.  37.  FIG.  38. 

We  have  : 

From  A  to  B.  Addition  of  heat  at  atmospheric  pressure. 
From  B  to  C.  Adiabatic  expansion. 
From  C  to  D.  Cooling  isopiestically. 
From  D  to  A.  Adiabatic  compression. 

CYCLE   VIII. 


FIG.  39. 


FIG.  40. 


We  have  : 

From  A  to  B.  Addition  of  heat  at  atmospheric  pressure. 
From  B  to  C.  Adiabatic  compression  to  such  a  pressure,  that 
we  get, 

From  C  to  D.  Isothermal  compression  to  original  state. 

CYCLE  IX. 


V 


FIG.  42. 


FIG.  41. 
We  have : 

From  A  to  B.  Addition  of  heat  at  atmospheric  pressure. 
From  B  to  C.  Adiabatic  expansion. 
From  C  to  D.   Cooling  isometrically. 
From  D  to  A.   Compression  adiabatically. 


CYCLIC    ANALYSIS    OF     HEAT    ENGINES.  21 

We  might  have  many  modifications  of  these  but  as  a  discussion 
of  the  type  throws  sufficient  light  on  the  variations  considering 
the  importance  of  the  cycles,  these  modifications  will  not  be  dis- 
cussed. 

CYCLE   I. 

Fig.   i.  Fig.  2. 

Let  HI  be  the  heat  added  from  B  to  C. 

Let  Cv  be  the  specific  heat  of  gas  at  constant  volume,  and  here 
assumed  constant  for  simplification.  It  is  probably  a  variable,  but 
so  assuming  it  gives  unmanageable  formulae.  A  correction  may 
afterward  be  applied,  if  desired.  Cv  =  heat  to  raise  one  pound 
gas  i  °  F.  at  constant  volume. 

Let  vb  be  the  volume  of  the  gases  at  point  B  of  the  diagram, 
i.  e.t  before  heating  and  expressed  in  cubic  feet. 

Let  pb  be  the  corresponding  pressure  in  pounds  per  square  foot. 

Let  Tb  be  the  corresponding  temperature  in  absolute  degrees 
Fahrenheit. 

Then  will  the  increase  in  temperature  be  given  by' 

T  _H\ 

<~    b~^v 
or 


Since  volume  is  constant  from  B  to  C, 


whence 

A-Af- 

y /> 
From  (i) 

£'-'*i-3L 

?;~    hc-X 

Since  this  quantity 


C.T; 


will  enter  into  many  of  our  equations,  let  us  denote  it  by 


whence 


22  THE    HEAT    ENGINE    PROBLEM. 

P.-PJ-  (2) 

The  adiabatic  relation 

p/>if 

gives 


But  pd  —  pb  by  hypothesis,  hence 

-^)^  (3) 

Another  adiabatic  relation  gives 


whence 


remembering  pd  =  pb  and  substituting  the  value  of  Te 


Let  H2  be  the  heat  discharged.     Then 


Where  Cp  —  specific  heat  at  constant  pressure  and  assumed  con- 
stant.    Hence  substituting 

-  1).     (s) 


The  work  done  in  heat  units  will  be 

W-H^-H,         i  (6) 

~Hl-CfTJ<X^-iJ.  (7) 

And  in  foot  pounds 


This  work  of  expansion  could  have  been  obtained  by  tempera- 
tures and  by  integration  as  well. 
We  have 


CYCLIC    ANALYSIS   OF   HEAT   ENGINES.  23 

But 


..IT-  CTf-CTb-C,Td+ 
We  know  also 


and 


in  heat  units.     This  second  term  is  the  area  of  the  rectangle  be- 

tween   {  *  =  °  and  \V  ==  V*  and  lying  below  atmos- 

(  /  =  atmosphere  (  v  =  vd 

phere  is  not  available  for  work. 

By  integration  W  —  j^°  pdv  =  area  between  expansion  curve 
and  axis  of  volumes.     The  expansion  is  adiabatic. 


i  —r         i  —  r 

/£/„  —  ^  ^ 

.         yy    •      =  tf       «»  _  £-£_C 

i  -r 

Since 


c,  c, 

=  JCv(Tc  -  Td)  in  foot  pounds. 
Subtracting  the  rectangle  pb(vd  —  vb)  we  get 


24  THE  HEAT  ENGINE  PROBLEM. 

in  foot  pounds,  or  in  heat  units 


as  before. 

Before  going  farther  let  us  apply  a  test  to  each  of  the  states  B, 
C,  D  from  the  law  of  perfect  gases 


*  bb  _       bb  __    r, 

=  "      Tb  - 


T  l  '      T 


r, 


hence  these  are  identities,  as  they  should  be. 

Denote  the  volume  swept  through  or  volume  range  by  Rv. 

Then  will 

i_ 

R*  =  vd-vb  =  vd-vc  =  vb\Xi  -  i]  (8) 

Whence  mean  effective  pressure 


Efficiency 

The  entropy  range  is  given  by 
Mean  effective  temperature 

The  temperature  range 
The  pressure  range 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  25 

Whence  we  may  write  a  mean  effective  volume 


MEV  7 

-       -J 


-  i).  (16) 

These  results  are  here  tabulated  for  reference  and  comparison 
with  what  follows  : 

We  might  take  the  formulae*  derived  for  mean  effective  tempera- 
ture, but  as  these  were  the  results  of  a  comparison  of  cycles,  none 
of  which -ran  below  atmospheric  pressure,  it  would  be  better  to 
take  another  standard  here.  Let  us  take  arbitrarily  as  the  mean 
effective  temperature  one  half  the  sum  of  the  mean  temperature 
of  heat  addition  and  the  mean  temperature  of  heat  abstraction. 

CYCLE  I.        X=  i  +  -— L 


Formula  Reduced  to  Initial 
Symbol.  Formula  as  Derived.  Conditions. 

'6 Arbitrary ph 


B 


*T*  x  b     b  *   b     b 

b"  ~R   '  ~R~ 

T 
p p.-^ p.X 

t  e  to    i  *  b 

*  b 


T 


D\ 


Pa Pb 


a 

T< MA' r"Xy 

H, Cf(Tt-Tb) CT^-  i) 

W J(H,-H^ .J{ff,  -  Cp 

*  School  of  Mines  Quarterly,  XXI.,  4,  1900. 


26  THE    HEAT    ENGINE    PROBLEM. 

Formula  Reduced  to  Initial 
Symbol.  Formula  as  Derived.  Conditions. 


E 

'-' 


*. *«-'*„ ^Y-I) 

M.E.P..  ./£ 


*, A  -A A(^-  0 

FT 


M.E.V. 


R* £k&r ^log«^ 

i 


7; 


r  ................  Tc-Tb  ..............  Tb(X-i). 

CYCLE  I.  A. 

FIG.  3.  FIG.  4. 

We  have  as  in  Cycle  I.  for  point  C. 

vc  =  vb  (i) 


(3) 
Assume 


Then  from  the  adiabatic  relation 

v 


or 
Also 

"v*>  (s) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  2/ 

Substituting,  values  of  pc  and  Tc  in  (4)  and  (5)  we  get 


**£(0'  (6) 


T<-T*\-&)*  -T^\jr-        (7) 

If  we  write 

j-"' 

A 

then  JL_ 

7  (8) 


(9) 

ff 

l_ 

ve  =  vd  =  vb(Xn)y,  (10) 

A -A. 


.  (u) 

6 

Let  us  apply  the  perfect  gas  law  to  the  points  B,  C,  D  and  E. 

A?h  r> 

-r  =  A, 


/•^c    c         fb         b  r> 

^r~ =  ~T~y  =  R> 

J.  J.  i^A. 

c  o 


l  r, 

— 


T 

* 


Heat  is  abstracted  in  two  parts,  the  first  at  constant  volume 
from  D  to  E  and  the  second  at  constant  atmospheric  pressure 
from  E  to  B. 


28  THE    HEAT    ENGINE   PROBLEM. 

Hence 


The  work  done  in  foot  pounds  is 

(13) 


(«4) 

('5) 


The  mean  effective  pressure 

W 

M.E.P.  =  -£-.  (16) 

But 


,M.E.P,«/|-  -j-  K(i8) 


r 

C  1  /  i  \  11 

I  JLJ  £  T (Xn\i  I  - I  I  -4-  ^*  7"  ff^Y??^  il   I 

II  »   b  \n          j         P   b  j. 


(2( 


As  before,  the  entropy  range  is 

R^=Cv\ogX.  (21) 


CYCLIC   ANALYSIS    OF    HEAT    ENGINES. 


29 


Taking  the  mean  effective  temperature  as  the  mean  of  the  aver- 
age heating  temperature  and  the  average  cooling  temperature, 


C.\og.X 


The  temperature  range  is 


The  pressure  range  is 


Whence 


•    (23) 

(24) 

(25) 


/ 


'.)7  (I-:)- 
'     \n         1 


(26) 


Tabulating  these  results  we  get  for 

CYCLE  I.  A. 

Symbol.       Formula  as  first  derived.  Formula  reduced  to  initial  condition. 

pb  ----  Arbitrary  ----  .  .................  pb 


B< 


C 


T 


A 


R 


R 


THE    HEAT    ENGINE    PROBLEM. 


Symbol.       Formula  as  first  derived.  Formula  reduced  to  initial  condition. 

i 


D\ 


E\ 


A 

v. 


E 

R  . 


M-KP R- 


H-2 

*  T 

—      ,-  -r    •    •    •    •    1    ~— 


ff,..C.(Ti-T)+  C(T-Tt)~C.Tt(Xn)->  \--i\- 


MET 


A  -A 


«)7g-  i)  -CfT&Xnji-  i] 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  31 

CYCLE  I.  B. 
FIG.  5.  FIG.  6. 

As  the  operations  up  to  the  point  C,  i.  e.,  after  addition  of  heat 
are  the  same  as  in  cycle  I.,  we  may  assume  these  results  : 

Ve=Vl»  (0 

A  =  A*  (2) 

T.=  TbX.  (3) 

Choose  pd  so  that 

A>A>o-  (4) 

Expansion  CD  gives 


Also 


From  the  isothermal  relation  along  DE, 


A  =  A  by  hypothesis  (8) 


or 


Applying  the  perfect  gas  law  to  the  various  points 


T         T,X  ~  '   T, 

cb  b 


32  THE    HEAT    ENGINE    PROBLEM. 


i)  v         b  b      n  i)^v 

fe    e  ___    fb    b  __    r> 

-jT  =  ±     •-     ••    -~-  -—   ^-. 

'•         T(XnT  b 

^      n 

Heat  is  abstracted  in  two  parts,  first  a  part  isothermally  and 
second  a  part  at  atmospheric  pressure.  The  part  abstracted 
isothermally  is  extremely  difficult  to  calculate  without  the  aid  of 
the  60  diagram  and  its  relations. 

The  entropy  range  along  BC  has  been  found  to  be 

« 

Now  it  is  evidently  the  same  so  far  as  entropy  range  is  con- 
cerned whether  we  cool  at  constant  pressure  from  E  to  B  or  heat 
isopiestically  from  B  to  E,  thus 

Tf 

Hence  the  entropy  range  for  the  isothermal  operation  will  be 
given  by 


(.3) 

This  latter  isothermal  change  taking  place  at  temperature  Te  = 
Td  the  heat  of  cooling  will  be  given  by 


Hence  the  total  heat  abstracted  is 


=  Cp(Tc  -  Tb)  +  T,  \  C,  \ogcX-  Cp  log  5]         (15) 

«-  •*•  'h  J 


But 


_£ 

Cf  l°S, "~  =  Cr  loge  X V  +  Cf  log, »  i 
=  C,\0geX+(C,-Cp)l0g. 


,,. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


33 


Since 


And 


Hence 


The  work  in  foot-pounds  is 


-*.        (16) 


(17) 


-.£=  I  - 


(18) 


M.E.P.  =/ 


.-.  M.E.V.  =/] 


(20) 


(21) 


(22) 


The  mean  effective  temperature  being  the  mean  of  the  heating 
and  cooling  means  is  given  by 

M.E.T.  = 


where  R^  is  same  as  in  previous  cycle. 


34  THE   HEAT   ENGINE   PROBLEM. 


log 

(23) 


Tabulating : 

* 

CYCLE  I.  B. 

Symbol.     Formula  as  first  derived.  Formula  reduced  to  initial  conditions. 

pb Atmosphere Atmospheric  pb 

vb Arbitrary vb 


c 


"    R                                             '   R 
A A? A* 


Tt(Xn) 


A 


T, 


CYCLIC   ANALYSIS   OF   HEAT   ENGINES. 


3S 


C,(T.-Tt)  +  7-Jc.log.A--  C,log.£ 


w. 


I  — 


-  ».)  ..............  ^[(- 


M'E-P 


-A 


-  A 


M.E.V. 


log,  5 


T, 


M.E.T. 


36  THE    HEAT    ENGINE    PROBLEM. 


CYCLE  I.  C. 

FIG.  7.  FIG.  8. 

Assume  all  results  to  point  C  from  Cycle  I. 

A  -A*  (0 

"<  =  ^  (2) 

T.~T,X.  (3) 

From  the  adiabatic  CD. 


This  adiabatic  must  meet  the  isothermal  from  B  in  point  Z>, 
hence 

'I   ;'        ^-^^-  -   ;-      (5) 

Equate  (4)  and  (5) 


(6) 


This  is  the  pressure  at  which  the  isothermal  through  B  will 
meet  the  adiabatic  through  C.     Its  corresponding  volume  is 

*<  =  »,  -      =  ^^  (7) 


T*-1v  (8) 

The  heat  abstracted  by  the  isothermal  cooling  is  found  as  before 
from  60  relation. 

=  c\o     Tc=C\o    X. 

6  * i 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  37 

Hence 


logeX.  (n) 

The  work  done  in  foot-pounds  is 

W=J(H,  =  /Q  =/(//,  -  7;C.log.Jr>  (12) 

The  efficiency  is 

The  volume  range  is 

i  • 

Hence 


The  entropy  range  was  found  R^  =  Cv  logc  X  hence 

M-[-«  »-p<          •«  /  •***    i"  •*•  V 
.E.T.  = 


The  pressure  range  is 

Xr* 


And 

Tabulate 

CYCLE  I.  C. 

Formula  reduced  to  initial 
Symbol.  Formula  as  first  derived.  conditions. 

pb Atmospheric Atmospheric/^ 

vb Arbitrary vb 

Tb J? ~'R 


THE  HEAT  ENGINE  PROBLEM. 


P'ormula  reduced  to  initial 


Sym 

c- 

D 

bol. 

Formula  as  first  derived.                               conditions. 

Tb 

•f  c  

"V 

f  b    y                                                                        f  b 

c 

.  .V  .                                                         .  V 

T 

T1  I  T  _i_         1    l                                           TV 

4) 

*V  h  C,TJ- 
I   A    j                                   A 

Pd'  '  ' 
1) 

1                                                                                   1 

T,. 

b                                                                                 b 

....Wog.y' V.log^ 


E. 
R 


H 


M.E.P  ............  ....-    ......  ......  / 


M.E.V. 


>.  - 


M.E.T. 


.'.  •  T-  TI:  : .'....  .T,(X- 


CYCLIC   ANALYSIS   OF   HEAT   ENGINES. 


39 


CYCLE  II.* 

Let  Fig.  9  be  the  P.  V.  and  Fig.  10  the  0<P  diagram  of  this 
cycle. 


P         iC  CYCLE  H 


e. 


B 


V 


FIG.  9. 


FIG.    IO. 


In  the  compression  cycles  the  volume  ratio  —  will  enter  into 
many  of  our  formulae  and  we  will  find  it  convenient  to  write 

-  =  r- 

The  compression  is  adiabatic,  hence 

..  _;.     A=A(^)V  =  /^  (i) 

r.-Mjr- 


During  addition  of  heat  vc  =  vb  and  therefore 


School  of  Mines  Quarterly,  Vol.  XXII.,  April,  1901,  No.  3. 


40  THE    HEAT   ENGINE    PROBLEM. 

T  J-f 

If  we  write  ~  =  I  +  =  X  as  in  the  previous  cycles  we  get 


(3) 
(4) 
Adiabatic  expansion  gives 


V  =  VX  V  =         ^^  =  ^  *  •  (5) 


(6) 

a 

Applying  the  perfect  gas  law 


q  r, 

-- 


d  aa  _      J? 

T  ~~  1    ~ 

"      r^v 

The  heat  discharged 

H2  =  C,(7i  -  TJ  =  C,T.(X$  -  i).  (7) 

work  done  is 

W-  H,-Ht~H,-  CpTa(X^   -  i)  (8) 

W  CT(X^i  -  i) 

£  =      =  1-^'-  9) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  41 


<"> 


(12) 


(H) 

(i5) 


CYCLE  II. 

Symbol.  Formula  as  First  Derived.  Formula  Reduced. 


».  ..............  -'  frarbitrafy) 


T  M 


A AV 


42  THE    HEAT    ENGINE    PROBLEM. 

Symbol.  Formula  as  First  Derived.  Formula  Reduced. 

Pi Pa A 


H, -Cr(Td-Ta) < 

w. fft-fft HI-  £>7i<jrv  - 


w  H.-CTJ.XI-I) 

M-E-P JR /-^-tr 


M-KT 


.log.      ..............  C,\ogX 

2  b 

-0 


R.  ..........  ..-....•  -A  -A  .........  .-.••-•  -pa(rx- 


7;-  r 


CYCLIC   ANALYSIS    OF   HEAT   ENGINES. 


43 


CYCLE  II.  A. 

Let  Fig.  ii  be  the  P.  V.  and  Fig.  12  the  6(P  diagram  for  the 
cycle. 


p        ,C-         '„    CYCLE  11A. 


V 


FIG.  n. 


FIG.  12. 


Then  we  have,  since  the  compression  is  as  in  Cycle  II., 


-« 


A=Arv. 


Also  for  C  the  heat  addition  being  as  before 


(0 

(2) 

(3) 


(4) 

ill .        (s) 

~1X.  (6) 

The  point  D  lies  arbitrarily  between  C  and  the  atmospheric  line 
on  the  adiabatic 


(V 
^r 


-.      (7) 


From  this  point  we  will  consider  two.  cases:   i°,  the  general 
where  vd  is   greater  than   va,   and   2°,  a  particular  case  where 


44 


THE    HEAT    ENGINE    PROBLEM. 


Then  we  have 


Y-l 


v  V*-1 


P.=Pa 


(8') 


(9) 

T  f          TV 
j    ==  •*    •*'*• 

(9') 

(10) 

V.'  =  ""a 

(10') 

(n) 

A'=A 

(ii') 

'A 


*> 


(12) 


(12') 


Apply  the  perfect  gas  law 


AT' 


R, 


R. 


<-R, 


p'v'       v  p 

*«      <    __       a^o-   .  J£ 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  45 

Heat  is  abstracted  as  follows  : 


The  work  is  given  by 


(H) 

-V- 1?-]- 

Volume  range  is 

j 

R,  =  vd-vb  =  vd-^      (is) 

w        w 

M.E.P.  =/__=/---     (I6) 


(13') 


C.TJX-  i]. 


M.E.P.=/ 


Entropy  range  is  the  same  for  both  cases, 


46 


THE    HEAT    ENGINE   PROBLEM. 


Mean  of  mean  temperatures  of  heat  addition  and  abstraction, 

M.E.T.' 


MET  - 

-' 


2  C,\Og,X 


(18) 


(i  8') 


Pressure  range  is  same  for  both  cases 


Mean  effective  volume 
W 


(19) 


^  (20) 


Temperature  range  is  also  the  same  for  both 


w 


(21) 


CYCLE  II.  B. 


Let  Fig.  13  and  Fig.  14  be  the  P.V.  and  0<f>  diagram  respec- 
tively of  the  cycle. 


CYCLE  ITB. 


0 


B 


c. 


E. 


FIG.  13. 


FIG.  14. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  47. 

Assume  same  results  as  before  up  to  the  point  c.     Take   pd 
something  less  than  atmosphere,  i.  e., 


0-  (0 

Then 


And 


Through  D  and  a  point  E  whose  volume  is  greater  than  the  orig- 
inal we  have  an  isothermal 

(4) 


*•  '"'/."'M  A  r/, 

Hence 


A  =  A-  (6) 

Apply  the  perfect  gas  law  to  the  points 

p  v 
a  n  —  f? 


i      i 

A 


T 


AA_  o 

r  "  ~    • 


48  THE   HEAT   ENGINE   PROBLEM. 

During  the  isothermal  compression  heat  must  be  abstracted,  the 
amount  can  best  be  calculated  by  Oy  coordinates.  Call  this 
amount  w,  then, 

m  = 


But 

f!t-  f.=  Cfe-  f»)  ~  (f.  - 

and 

" 


Besides  this  amount  m  we  must  abstract  a  quantity  £^(7^  —  7a) 
isopiestically,  whence 


,  =  CJtT.  -  T.)  +  T,  j  C.  log,X+  Cr  log.  \X^  (  g)*T  ]  J 

(7) 


»•-//,-//„  (8) 

£-l~Wt-  (9) 

The  volume  range  is 

(10) 

(II) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


w 


49 


(15) 


CYCLE  II.  C. 

i 

Let   Fig.  15  be  the  P.V.  and   Fig.  16  the   60  diagrams  of  the 
cycle. 

CYCLE  JIG 


FIG.  15. 


FIG.  16. 


All  values  for  the  compression  and  heat  addition  found  in  Cycle 
II.  may  here  be  assumed.  The  point  D  lies  at  the  intersection  of 
two  curves,  one  an  adiabatic  through  C,  the  other  an  isothermal 
through  A  and  the  relations  can  be  written.  From  the  adiabatic 
relation 


From  the  isothermal  relation 


Equating  we  get 


50  THE    HEAT    ENGINE    PROBLEM. 


Pa 

This  is  the  pressure  at  which  the  intersection  will  take  place. 
By  substitution  we  get 

^-f.AFi  -."  •  "    (2) 

;  Td-T,      .  '-    \  (3) 

Applying  the  perfect  gas  law  to  D 


-K. 


All  the  heat  is  abstracted  at  constant  temperature  during  the 
compression  D  to  A.  The  entropy  range  is  evidently  the  same  as 
for  heat  addition  and  this  is 

R<p-C.\og.X  (4) 

whence 

tf,=  7-.(P--«O=Wog.A-  (5) 

work 

W=H,-  H2  =  //,  -  T.C,  log,  X  (6) 


0) 


whence 


(9) 


CYCLIC    ANALYSIS  OF    HEAT    ENGINES. 


Tabulate. 

Symbol. 

A 


Tc 

P,r 

va< 
T, 


W. 

£.. 


RT=  Ta(y-\X-  i)     as  before 


CYCLE  II.     C. 

Formula  as  first  derived. 
y 


V 


(v  \y~* 
n 
*^h ' 


T 


(12) 
(13) 


Formula  reduced. 


!i 
r 


•Pa' 


T 


Tn(y>d  —  <pa) 7^6^  loge  X 


i  — 


H, 


52 


THE  HEAT  ENGINE  PROBLEM. 


R 


W 


M.E.P /" / 


M.E.V, 


R. 

•A  -A 
-W 


R 


CYCLE    III. 

Let  Fig.  17  be  its  P.V.  and  Fig.  18  its  60  diagram. 
CYCLE  ffl 


FIG.  17.  FIG.  18. 

The  compression  results  of  Cycle  II.  may  be  assumed,  hence 

(0 

(2) 

(3) 

Heat  is  added  isopiestically,  hence  calling   Cp  the  specific  heat  at 
constant  pressure  we  have 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  53 

Write 


(s) 
".-^-^--•K  (6) 

•*•  b  f 

Adiabatic,  expansion  gives  for  final  pressure  of  one  atmosphere 


A=A  (8) 


•••T,=  TaY=-f-lT,  (9) 

Apply  the  perfect  gas  law 

PaVa   __  R 

~r;~ 

=  R  as  in  II. 


py, 

T 


T 


Hence  the  formulae  are  verified. 
Heat  is  abstracted  isopiestically 


=  CpT.(Y-  i)  (10) 

i)  (n) 


W  H,  CT(Y-  i) 

_  _    T  2  _    T  p     a\  _  / 

-  - 


54  THE  HEAT  ENGINE  PROBLEM. 

Volume  range  is 

Xt-vt-vt  =  v,(Y-1-)  03) 

Whence  for  mean  effective  pressure 


T, 


A 


T 


<«, 

(17) 


F-.).  (19) 

Tabulate. 

CYCLE  III. 

Symbol.  Formula  as  derived.  Formula  reduced. 


A ••! 

V  V 

V... -* -tt 

r  r 


'd 


.*£ s?r 

s^  r 


T: : 

A A 


*„ f.tSt» *< 

^*a 


(^    \   Y"1 
^) 


CYCLIC  ANALYSIS  OF  HEAT  ENGINES.  55 

Ht Cf(Tt-Tj CfTa(Y-  i) 

w Hl-H2 *;'-  crr,(Y~  i) 

fft  CT(Y-  i) 


E. 
R<p 


C 


M.E.T. 


R<f 


••Cploge 
ii-^/1 


<P-7 


M.E.P. 


y 


, A -A A(rY- 

^F 


M.E.V. 


/ 


CYCLE  III.  A. 
Fig.  19  is  its  P.V.  and  Fig.  20  its  60  diagram. 


CYCLE  HI  A 


FIG.   19. 


e 


FJG.  20. 


Assume  the  results  of  III.  up  to  point  C.  The  point  D  is  situ- 
ated anywhere  on  the  adiabatic  through  C  between  C  and  atmos- 
phere. 


56  THE    HEAT    ENGINE    PROBLEM. 

Write 

Pc>Pd>Pa  (0 

and 

V*>Va-  (2) 

This  latter  (2)  will  not  necessarily  follow  from  (i)  but  where  it 
does  not  hold  the  cycle  is  decidedly  imperfect  and  this  case  is  here 
neglected,  i.  e.,  the  case  where  the  isometric  DE  cuts  the  adiabatic 
AB. 

We  have  then 


P.-  P.  (5) 


Apply  the  perfect  gas  law  to  D  arid  E. 


AA 
r 


This  verifies  the  formulae. 

Heat  is  abstracted  in  two  parts  and  the  amount  is 


(8) 


CYCLIC  ANALYSIS  OF  HEAT  ENGINES. 


57 


-'} 


The  work  done  is 
and  efficiency 


-  H 


Hn 


W 


W 

:.E.P.  =  /^-  = 


Rtp  —  Cp  \oge  Fas  before  for  III. 

RP=  P-  Pa  =  P«(ry  -  i)     as  in  III. 
•  M  F  V  —  / / — — 

-JRr-Jp.(r-ir 

As  before  III.  the  temperature  range 


CYCLE  III.  B. 
Figs.  21  and  22  are  its  diagrams 

P  CYCLE    MR  a 


B 


A.  E. 


(10) 

(II) 

(12) 
(13) 

(14) 
(15) 

(16) 


(18) 


FIG.  21 


FIG.  22. 


58  THE    HEAT    ENGINE    PROBLEM. 

All  results  of  III.  A  up  to  period  D  may  be  assumed  except 
that  pd  which  was  there  arbitrary  was  assumed  greater  than  pa  is 
here  less  than  pa,  i.  e., 

pc>pd>o.  (i) 

We  had 


and 

/AiY~~l.  (3) 


'  \P. 
Through  E  and  D  there  must  pass  an  isothermal  and 


l'e          Vd  p     "        C'd  p     ~      Va        \  p     ]       p 
re  -fa  -f  d          *a 


.•  .   (;) 

Applying  the  perfect  gas  law  to  E 


Heat  abstracted  I  °  isothermally  a  quantity  ?«. 
2°  isopiestically          "  n. 

n=Cp(Te-Ta) 


But 


(4) 
(5) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


59 


=  H,  -  Hv 


(10) 


M.E.R=/^=y 


w 


=y/>-/; 

r  =  Ta(-{*-1  Y-  i)     as  before  III. 


CYCLE  III.   C. 
Let  Figs.  23  and  24  be  its  diagrams. 

CYCLE  inc. 


A. 


FIG.  23- 


V 


(13) 
C4) 

(15) 


(17) 


G 


D. 


FIG.  24. 


6o  THE    HEAT    ENGINE    PROBLEM. 

We  will  assume  all  results  to  C  already  derived.  The  point  D 
is  determined  by  the  intersection  of  the  adiabatic  through  C  with 
the  isothermal  through  A.  From  the  adiabatic  relation 


From  the  isothermal  relation 


yy-i 
By  substitution 


r  i  Pi 

-•      :   ,  .",       -*'  (0 

:    :       -  (2) 

";  (3) 

log,  Y  (4) 


(6) 


FT-' 


(8) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  6 1 

M.E.T.  =  i  (3+3)  =  *  (3r  f^r\ 

*  \      Ry      J       2  \         (7  log  F        / 

(10) 


+ 


=  7:-r  =  7;[rv-iF-i]asinIIL  (n) 

CYCLE  III.  C. 


Symbol. 

Formula  as  First  Derived.                           Formula  Reduced. 
ft    1  _?Ll                                                                   v,  ry 

\V   1 

Va                                                                                 Va 

b 

T  . 

f                                     r 

.7^  f5A  ;                                              Trv-1 

P  • 

a  \  ?;  /                                                              ft 

re 

-*    ft                                                                                                                                 /    rt/ 

„  ^                                               v«  F 

c     * 

T  .  . 

6^>                                  r 

r  (i  +        1   \  .                                   T  r^-1  F 

*\         i    T  t                                      l 

y_ 

i)    T^V—  ! 

v  . 

'   'fa1 

d 

T}. 

d 

T 

E 

<i 

•  ...ff.-ff,  ff1-T.cr\os.Y 

Rw  . 

.  C  log-  —c                                  C  loo-  F 

MET 

p    ^£>e  'p                                                                 P        fc>e 

2    \          ^?t£:          /                                         ^    y  £    IQCT    F             a  / 

62 

#r 

M.E.P.. 

R, 

M.E.V. 


THE    HEAT    ENGINE    PROBLEM. 
..*,-*..  ...  (Yri-L\ 

a\          r ; 

H.-T^rio 


J-i 


R 


J 


A-A p\r- 


yy-i 


T  -T 


CYCLE  IV. 

Figs.  25  and  26  are  its  diagrams. 
p     B.  CYCLE   IV  ©• 


B 


FIG.  25. 


FIG.  26. 


We  may  assume  the  results  already  obtained  for  the  compres- 
sion but  beyond  that  new  conditions  arise.  By  isothermal  heating 
the  curve  approaches  the  atmospheric  line  and  there  will  be  a  cer- 
tain quantity  of  heat  that  will  bring  the  isothermal  down  to  the 
atmospheric  line  leaving  a  subsequent  adiabatic  expansion  an  im- 
possibility. This  quantity  of  course  depends  on  the  location  of  B, 
i.  e.,  the  amount  of  previous  compression.  The  higher  the  pre- 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  63 

vious  compression  the  more  heat  may  we  add  isothermally  before 
reaching  atmospheric  pressure. 

The  quantity  of  heat  which  will  make  adiabatic  expansion  im- 
possible and  stop  the  isothermal  on  the  atmospheric  line  can  best 
be  determined  from  60  relations.  Denote  this  quantity  by  Q. 


FIG.  45. 


On  the  80  diagram  Fig.  45  the  point  3  lies  at  the  intersection 
of  the  isothermal  23  drawn  at  temperature  02  the  compression 
temperature  and  the  isopiestic  13  drawn  from  atmospheric  tem- 
perature Oi  to  the  intersection  3.  In  each  case  the  entropy  range 


C 


.-.  <2  = 

Apply  now  to  the  Cycle  IV. 


•*  i 
T, 


iogeTy  l.  (0 

This  is  the  amount  of  heat  that  will  bring  C  down  to  atmosphere 
with  no  adiabatic  expansion.  In  order  that  the  cycle  may  exist 
according  to  the  hypothetical  definition  we  must  add  less  heat 
than  this  quantity  Q.  Hence  we  have  the  equation  of  condition 
for  the  existence  of  the  cycle 


(2) 


or 


46  THE    HEAT   ENGINE   PROBLEM. 

A  similar  method  can  be  used  to  find  the  amount  of  expansion 
or  resulting  pressure  and  volume  after  addition  of  Hiy  BTU  of 
heat. 

Draw  on  both  diagrams  the  isopiestic  through  the  termination 
C  of  the  isothermal  and  cutting  the  adiabatic  AB  at  point  c'. 

Then 


T  T 

Y't  =  CP loS'  T, 

T  ry~l 


But 


And  the  amount  of  heat  necessary  for  this  isothermal  expansion 
from  B  to  C 


But 

r  -  i      £  -  '      C  -  C 


c 


and 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  65 

Put 


•n,      •„ 

Then  will 


That  is  to  say  if  we  start  at  state  B  and  add  a  quantity  of  heat 
Hv  isothermally  the  resulting  pressure  is 

A        P  Ty 

L     r  b  __    *  at  .,     v 

C  x»^5  /?  \  3 ) 

Since 


Now 


-  Q 


117         1  1     TTT 

We  had  III., 

Hence 

Whence 


(4) 

(5) 
(6) 


(7) 


66  THE    HEAT   ENGINE    PROBLEM. 

Similarly 


Apply  the  perfect  gas  law 


T. 


R 


f-fzr-R. 


Verifying  the  formulae, 


E 


l  — 


H 


-'  + 


M.E.P. -/£-/-       -^ 


(8) 


(9) 

(10) 


(12) 


ap^J    ;  03) 

(H) 


(15) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  67 


MEV        TW      jH.-C,W*-*)  ,     } 

-J  R-J      pa(r-i} 

-i).  (18) 


CYCLE  IV. 

Symbol.  Formula  as  Derived.  Formula  Reduced. 

A - M£)* W 


r 


T,, T^      Tjr 

T 
Equation  of  condition. .  .  H^  <  Tb\oge^  .  .  .  Hl  <  Tj*~l 

A  Pjy 


T, T, 

p p p 

id  fa  fa 


7, : 

H, Cp(T,-Ta) CpT.(er-1  -  i) 


i-g i  -  C,T.(<'-1  ~  0 


r>  "1 

^* 7; r-lf 


68 


THE  HEAT  ENGINE  PROBLEM. 


M.E.T r-vl-inf 

V 

J  r-p  j  j  x--    /y~i    /      Y 1  \  -, 

"T^l"      JL^~ 

» (l          V^ 

W  r// 

M-E-P JR, J\-v{e^_ 

r 

w 

M.E.V..  .../„ 


CYCLE  IV.  A. 
Figs.  27  and  28  are  its  diagrams. 

„  CYCLE   IVA,  8. 


B 


FIG.  27. 


E. 


FIG.  28. 


We  may  assume  the  results  of  IV.  up  to  point  C.  The  point 
D  lies  somewhere  on  the  adiabatic  between  C  and  atmosphere  and 
is  subject  to  the  conditions 

P.>P»>P.  (0 


CYCLIC    ANALYSIS   OF    HEAT    ENGINES.  69 

*.>•*  (2) 


Then 


r~':  •'••    .  (3) 

Similarly 


(4) 

(5) 


Apply  the  perfect  gas  law  to  D  and  E. 


T    '         JL 


The  heat  abstracted  is 


(7) 


THE  HEAT  ENGINE  PROBLEM. 


M.E.P.=/ 


W 


(8) 
(9) 

(10) 


M.E.V.  =  / 


w 


CYCLE  IV.  B. 

Let  Figs.  29  and  30  be  its  diagrams. 
B.  CYCLE   IVB 


B 


FIG.  29. 


FIG.  30. 


(12) 


(H) 


c 


D. 


FIG.  29.  FIG.  30. 

The  operations  up  to  C  are  as  in  IV.  and  we  may  assume  those 
results. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  /I 
The  point  D  is  subject  to  the  condition 

Pa<Pa  (I) 
and  the  point  E  to  the  condition 

Ve  >  Va-  (2) 

Then 

V    =  V    I  — "  I  V  €  *'~~1  f  7  ^ 

a  \  P    j  ^    ' 

and 

^-^"r-i  /\ 

^  (4) 


Following  the  methods  already  adopted  we  can  write 

ffi-Tfa-ri+Ctf-Tj. 

But 

<P<i  -<P,=  (<fc  -  <ft)  -  (<P.  -  <P,,) 


(8) 
(9) 


THE    HEAT    ENGINE    PROBLEM. 


•.M.E.P.  = 


w 


-    - 


Ri 


M.E.T.  = 


*      J 


CYCLE  IV.  C. 
Let  Figs.  31  and  32  be  its  diagrams. 

p    \B.  CYCLE  IYG 


B 


A. 


(10) 


(14) 


(IS) 

(16) 


FIG.  31. 
Assume  results  up  to  C  as  in  IV. 


FIG.  32. 


CYCLIC   ANALYSIS    OF    HEAT    ENGINES.  73 

The  adiabatic  through  C  must  meet  the  isothermal  through  A 
to  locate  the  point  D. 

From  the  adiabatic  relations 


From  the  isothermal  relation 


(V 
- 


V      y  V 


By  substitution 

P        P 

,      r  a fjs  /^\ 

7\=r.  (3) 

o,  d  \  *J  / 

By  inspection  it  is  easily  seen  the  perfect  gas  law  is  satisfied. 

n  H,       TH, 


(4) 
(5) 


(7) 

(8) 


74  THE    HEAT    ENGINE    PROBLEM. 

Rp=-.pb—  pd  =  p(fi  —-g\  (9) 

M.E.V.  =/- 

i 

M.E.T.  =  A(T;  +  T;)  --•(!  +  r-1)-  (10) 


CYCLE  IV.— C. 

Symbol.  Formula  as  Derived.  Formula  Reduced. 


A 


•>•(£)'• 


'»• 


r  r 


T; 711- 


(y 

Equation  of  condition Hl  >  o 

A 


W h 

E..  .1 


bpc '  r 

T..  .71.  .7>> 


A 

.z;^ 

« 

r 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


75 


1 
M.E.T *  '^"^) f°(l  + 

f 

M.E.P J~ JHA 

-•       -   ,  ||t'    I 

-#  .  .  ^  —  A .  -P  \ry  — F  I 

p  -fd          ft  -fa  \'  g%   I 

M.E.V /-^r 

•  -p 

^r T.-T, 


CYCLE  V. 
Let  Figs.  33  and  34  be  the  diagrams  of  the  cycles. 

CYCLE  f. 


P 


FIG.  33. 


FIG.  34. 


If  we  add  heat  at  increasing  /,  v,  and  T  the  curves  of  states  will 
lie  somewhere  between  the  isometric  and  isopiestic  on  both  dia- 
grams and  the  cycle  is  somewhere  between  III.  and  II.  If  the 


76 


THE    HEAT    ENGINE    PROBLEM. 


heat  addition  took  place  at  decreasing  p,  increasing  v  and  y  the 
curve  of  states  would  lie  between  the  isopiestic  and  the  isothermal 
and  the  cycle  lie  between  III.  and  IV.  We  cannot,  however,  cal- 
culate the  appropriate  set  of  formulae  without  knowing  the  law  of 
variation  of  states.  The  number  of  ways  of  variation  is  infinite, 
and  while  any  one  might  be  assumed,  nothing  could  be  gained  by 
the  calculation  unless  the  law  of  variation  chosen  were  preemi- 
nently simple  or  maintains  in  practice.  Whatever  it  may  be,  how- 
ever, the  previous  discussion  will  enable  us  to  class  it  pretty  well 
without  entering  much  into  details. 

CYCLE  VI. 
Let  Figs.  35  and  36  be  the  diagrams  of  the  cycle. 

CYCLE  VI. 

0. 


P 


V 


FIG.  35. 

Heat  being  added  isopiestically 

71- 


FIG.  36. 


H\ 


T>  /  H\ 

=  T"  (  l  +  ~CT 

*  {^^J-  . 


(0 


The  point  C  lies  on  the  adiabatic  through  A,  hence 


(3) 


(4) 


T  = 


x 


(5) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 
The  perfect  gas  law  is  seen  by  inspection  to  apply 

-  n  =  c. 


77 


(6) 
(7) 


.\R<f= 


M.E.T.  = 


c-I/a='Z'«(;ir-    0 


M.E.P.  =/- 


M.E.V.-/ 


-=/ 


CYCLE  VII. 
Let  Figs.  37  and  38  be  its  diagrams. 

CYCLE   VB. 


A 


(9) 
(10) 

(,2) 

(13) 
('4) 

(15) 
(16) 


FIG.  37. 


FIG.  38. 


78  THE    HEAT    ENGINE    PROBLEM. 

For  B  as  before  we  have 


(i) 


(3) 

The  point  (7  lies  on  an  adiabatic  through  B  and  is  subject  to  the 
condition 

A,>A>o  (4) 


(5) 

(p  \v-* 
)v-  * 


But 
Hence 

^=?-  (8> 

Similarly 

Ta      Tb 

And 


(10) 


Cp\ogex  as  in  VI.  (13) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


79 


w 


W 


CYCLE  VIII. 
Figs.  39  and  40  are  its  diagrams. 

CYCLE  VIII. 


0. 


We  have  for 


FIG.  39. 


(15) 
(16) 


(18) 
(19) 


FIG.  40. 


(0 


(3) 

The  isothermal  through  A  intersects  the  adiabatic  through  B  to 
determine  C. 

From  the  adiabatic 


From  the  isothermal 


( 


But 


8o 


THE    HEAT    ENGINE    PROBLEM, 


v  1*1      v 


JL 


By  substitution 


(4) 


,  =  v,-v«=°v*(xy-i-  0 


(6) 
(7) 

(8) 

(9) 
(10) 


CYCLE  IX. 
Let  Figs.  41  and  42  be  its  diagrams. 

CYCLE  IX- 


p 


(12) 


V 
FIG.  41.  FIG.  42. 

Up  to  the  point  C  the  results  of  VII.  may  be  assumed. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  8 1 

The  point  D  lies  on  an  adiabatic  through  A  and  is  subject  to  the 
conditions 

v,=  v  (i) 

d  c  \     / 


(3) 


5  (5) 


(6) 


-Ht-H,-CT*    ?    r      i-~  (7) 


(8) 
^  =  6^  loge  x     as  before  (9) 

M.E.T.  =  i(^™)  (10) 


W 

:.E.P.=/-          -rr  («) 


^=A-A  =  A-^7  (13) 

(^ 

M.E.V.-/-     ~  (14) 

L  f     C 


RT  =Tb-Tn=  Ta(x-  i).  (15) 


82  THE    HEAT    ENGINE    PROBLEM. 

CYCLE  X. 

In  this  cycle  as  in  the  last  four  heat  is  added  at  atmospheric 
pressure,  then  follows  adiabatic  expansion  after  which  heat  is  ab- 
stracted according  to  some  law  as  yet  undefined.  Adiabatic  com- 
pression completes  the  cycle.  As  the  law  of  abstraction  of  heat 
is  as  yet  undefined  we  cannot,  of  course,  derive  formulae  for  the 
cycle  and  will  leave  its  discussion  as  we  did  Cycle  V. 

We  might  have  derived  formulae  for  the  imperfect  carrying  out 
of  cycles  VI.,  VII.,  VIII.  and  IX.  but  they  are  of  such  slight  im- 
portance in  practice  that  it  did  not  seem  desirable. 

Besides  the  twenty-two  cycles  considered  there  may  be  others 
due  to  the  combination  or  differentiation  of  these  typical  ones,  but 
the  object  of  this  paper  will  be  best  accomplished  by  a  study  of 
types,  the  non-typical  or  synthetic  cycles  having  been  omitted. 
The  method  of  study  here  set  forth  being  of  universal  application 
to  all  possible  cycles  will  furnish  means  of  reaching  a  clear  under- 
standing of  any  of  the  unconsidered  cycles  should  need  arise. 

COMPARISON    OF    CYCLES. 

Of  the  many  cycles  considered  we  will  choose  for  comparison 
only  those  that  might  be  called  the  perfect  cycles  because  accurately 
defined  and  these  are  Cycles  I.,  I.  C,  II.,  II.  A2,  II.  C,  III.,  III.  C,  IV., 
IV.  C.  The  atmospheric  cycles  are  of  comparatively  little  impor- 
tance and  will  be  neglected  in  the  comparison.  We  will  take  up 
each  variable  separately  and  study  its  value  in  the  different  cases 
by  formula  and  by  calculated  examples  expressed  in  curves  which 
are  then  the  graphical  formulae.  The  curves  given  are  approxi- 
mately correct  and  as  the  same  approximation  will  probably  main- 
tain for  all  the  cases  the  curves  will  serve  as  well  for  comparison  as 
if  absolutely  exact.  Two  cases  of  each  are  given,  one  with  com- 
pression 2  :  i  and  one  with  10  :  I  (volume  ratios).  Call  the  at- 
mospheric values  pa,  va,  Ta. 

TEMPERATURES  AFTER  ADDITION  OF  H^  B.  T.  U. 

Cycle. 


I.,I.C  Tc=TX=Ta     i  +       r  CO 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


«3 


ii., ii. A.,  ii. c 


(2) 


-T2T2 
I2C2. 


JSZTQI. 


300         400         900        <bOO 


III.,  III.  C 


IV.,  IV.  C 


T  = 


(3) 
(4) 


Using  axes  of  Tc  and  //"t  we  see  these  are  all  straight  lines 
passing  through  the  axis  of  temperatures  at  Tb  above  the  origin 
except  in  cycles  (I.,  I.  C)  where  the  intersection  is  at  Ta.  These 
lines  are  inclined  to  the  axis  of  H  and  make  with  it  an  angle  « 
such  that  in 


I.,  I.  C,  II.,  II.  A,  II.  C  tan«=7,. 

0 


(5) 


84  THE   HEAT   ENGINE   PROBLEM. 

and  in 

III.,  III.  C  tan«'=^- 

p 

while  IV.,  IV.  C  are  lines  parallel  to  axis  Hr 

These  lines  are  shown  in  Fig.  46  for  two  compressions. 


(6) 


PRESSURES  AFTER  ADDITION  OF  Hv  B.  T.  U. 


Cycle. 
L,  I.  C 


(7) 


II.,  II.  A,  II.  C 
III.,  III.  C 
IV.,  IV.  C 


'i^b 


A- A 


A 

.z 


A 


(8) 
(9) 

(10) 


Equations  (7),  (8). and  (9)  are  all  straight  lines,  (9)  being  parallel 
to  axis  HI  while  (7)  and  (8)  are  inclined.  Equation  (10)  is  an 
exponential  curve  sloping  down  to  the  right  and  concave  up  and 
asymptotic  to  axis  of  H  as  can  be  seen  from  the  derivatives 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 
dp  Ph 


85 


(c,- 


A 


ir\ 


dff*  t         

(Cp—  CyT*4ft~W 
These  formulae  are  given  in  Fig.  47  for  the  two  cases. 

VOLUMES  AFTER  HEATING  BY  Hv  B.  T.  U. 
Cycle. 


(12) 


106  200         500         4-00        600        COO         7CO         8OO        9OO         IOOO 


I.,  I.  C 

II.,  II.  A,  II.  C 

III.,  III.  C 
IV.,  IV.  C 


V    =  V 


v 


=  *.**  =  *, 


(13) 
(H) 

(15) 
(16) 


Formula  (13)  is  a  straight  line  parallel  to  H^  and  is  always  less 
than  (14)  which  is  similar  but  cuts  axis  of  Vc  at  a  point  vb  higher 
than  va.  Equation  (15)  is  a  straight  line  inclined  to  Hr  Equa- 
tion (16)  is  an  exponential  curve  cutting  axis  Vc  at  point  Vv  it  is 
concave  up  and  slopes  up  to  the  right  as  is  shown  by  the  derivatives 


86 


THE  HEAT  ENGINE  PROBLEM. 


These  curves  are  shown  in  Fig.  48  for  the  two  cases. 
TEMPERATURE  AFTER  EXPANSION. 

Cycle. 


(17) 
(18) 


I. 

I.  C. 
IS. 


(19) 

(20) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  87 

ii.  A  rd  =  rtx=  r.(i  +  jly  };  (22) 

H.  C  Td=Ta,  (23) 

III-  7"=r"v=T"(l+fJ-)'  (24) 

HI.  C  Tt-T.,  (25) 

IV.  r,  =  TV1""1  =  7V  ^n,  (26) 

IV.  C  Td  =  T,  (27) 

Curves '(19)  and  (21)  are  similar  in  form,  cutting  axis  Td  at  dif- 
ferent points,  however,  and  having  different  slopes.  It  is  easily 
seen  that  (21)  is  always  greater  than  (19),  also  that  (22)  is  greater 
than  (21)  since 


Both  (22)  and  (24)  are  straight  lines,  but  they  have  different 
slopes  through  intersecting  axis  Td  at  same  point 

(tandVA.  -^  =  -^7.,  (28) 

v     b          '  v 

(tan  <J)IIL  =  —  [^  .  (29) 

/         P 

whence  (22)  is  always  greater  than  (24).  Equation  (26)  is  an  ex- 
potential  cutting  Td  axis  at  Ta,  it  is  concave  up  and  slopes  up  to 
the  right  since 

l 


d2T 


These  curves  are  shown  in  Fig.  49  for  the  two  cases. 
PRESSURES  AFTER  EXPANSION. 

Cycle. 

I-  A  =  A-  (32) 


I.  C 


II. 

II.  A 

II.  C 

III. 

III.  C 


THE    HEAT    ENGINE    PROBLEM, 
P  P 

,,  -i  a  fa 


(33) 


Tl<3.  SO. 


A- A 


A 


(34) 
(35) 

(36) 
(37) 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


89 


IV. 
IV.  C 


A 


e(Cp-Cv)Tb 


(39) 
(40) 


Equations  (32),  (34),  (37),  (39)  are  identical  and  represent  a 
straight  line  parallel  to  axis  //r  Curve  (55)  is  a  straight  line  in- 
clined to  Hr  All  the  others  are  concave  up  sloping  down  to  the 
right ;  their  relative  positions  are  seen  in  Fig:  50  for  two  compres- 
sions. 

VOLUMES  AFTER  EXPANSION. 

Cycle. 


JSTC2 


I. 


(40 


90  THE    HEAT    ENGINE    PROBLEM. 

I.  C  •     *,  -  vX^  =  P.     I  +  fK  (42) 


II.  ^  =  V=^'+>.  .    (43) 

II.  A  vd  =  *'„,  (44) 

II.  C  vtl  =  s^  =  *.  (  i  4-  ^  )^,  (45) 

in.  f.,-».y;  (46) 

III.  C  vt  =  »„  Yri  -v.i  +  -"      ^,  (47) 


IV.  i.,  =  t^'-i  =  fcyVl,  (48) 


IV.  C  vd  =  vaez '  =  vae(Cp-c^T».  (49) 

These  curves  will  admit  of  considerable  discussion,  but  the  curves 
of  Fig.  5  i  show  at  a  glance  all  we  wish  to  know  in  general. 

HEAT  DISCHARGED  OR  ABSTRACTED. 

Cycle. 

I-  H2=  CpTa(Xy  -  i),  (50) 

/  H^\ 

>e\          C***'' 

II.  H2=  CTn(X-i  -  i),  (52) 

II-  A  H2=  CTa(X-  i)  =  ^,  (53) 
II-  C                       H2=CvTa\oge(i-^),  (54) 
HI-                             H^CTa(Y-i}^^                          (55) 

III.  C  H2  =  CpTa  loge  (  i  +  ^  ),  (56) 

*         ^p1*1 

IV  //  —  C  T (eY~l  —  T "\  —  C  T  (e^rb  —  1}  ( c 7") 

1  v  •  J'72 —  u»^«\^  1/' —  ^o2a\e  L J>  \5r) 


IV.  C 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


(58) 


Equations  (33),  (55)  and  (58)  are  identical,  that  is,  these  three 
cycles  will  discharge  the  same  amount  of  heat  and  have  the  same 
efficiency  ;  moreover  this  efficiency  will  be  independent  of  every- 
thing but  the  compression.  These  three  cycles  have,  further, 
a  common  property  not  seen  by  the  formula,  but  from  their  defi- 
nitions each  receives  and  discharges  all  its  heat  according  to  the 
same  law. 

-  Cycle  II.  A  receives  all  heat  at  constant  volume  and  discharges 
all  at  constant  volume. 

Cycle  III.  receives  all  heat  at  constant  pressure  and  discharges 
all  at  constant  pressure. 

Cycle  IV.  C  receives  all  heat  at  constant  temperature  and  dis- 
charges all  at  constant  temperature. 

A  consideration  of  the  above  would  seem  to  warrant  the  prop- 
osition : 

When  all  the  heat  is  discharged  according  to  the  same  law 
under  which  it  was  received  then  the  cycle  will  have  an  efficiency 
independent  of  everything  but  the  previous  compression  and  will 
be  given  by 


We  may  remark   here  that  as  IV.  C  is  the  Carnot  Cycle  we  can 
state  that  Cycles  II.  A  and  III.  have  the  same  efficiency  as  the 


92  THE    HEAT    ENGINE    PROBLEM. 

Carnot  Cycle  with  same  previous  compression.  This  is  an  im- 
portant supplementary  to  the  old  theorem  that  the  Carnot  Cycle 
has  the  highest  efficiency  for  its  temperature  range. 

The  relation  between  the  other  values  of  H2  are  best  shown 
by  the  curves  of  Fig.  52  by  implication.  The  quantities:  Pres- 
sure range,  Volume  range,  Temperature  range,  do  not  need  sepa- 


a  >* 


A  2 


100  300 


rate  sets  of  curves  as  we  can  get  a  fair  idea  of  the  values  from  an 
inspection  of  the  previous  curves.  If,  however,  any  case  seems  to 
call  for  an  exact  solution  it  can  be  obtained  by  a  simp'e  substitu- 
tion in  the  formulae  already  given. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


93 


Mean  effective  pressure,  volume  and  temperature,  however,  are 
important  values  and  not  easily  located  relatively  from  the  formulae. 
Figs.  53,  54  and  55  show  these  curves  as  calculated  for  two  cases 
of  compression.  It  may  be  here  remarked  that  in  the  case  of 
Cycle  IV.  when  the  compression  is  2:1  only  about  44  B.T.U.  can 
be  added  to  i  Ib.  air  and  with  a  compression  of  10:1  about  282 
B.T.U.,  this  is  why  the  curves  end  abruptly  at  these  values  of  Hr 


OIL2. 


C- 

3 

r 


3HQ2 


3HCI 


A  thorough  discussion  of  the  equations  derived  while  important 
and  leading  no  doubt  to  many  new  and  useful  results  would  be 
very  long  and  would  extend  beyond  the  limits  set  for  this  paper 
which  had  for  its  object  rather  the  exposition  of  the  method  of 
procedure  than  a  thorough  application  of  that  method. 

Besides  the  complete  discussion  referred  to  there  is  another  im- 
portant point  of  view  to  be  taken  of  these  formulae — that  of  inter- 


94 


THE    HEAT    ENGINE    PROBLEM. 


pretation  with  respect  to  operating  engines  ;  this  is  also  reserved  for 
later  treatment. 


irz 


The  curves  of  the  important  cyclic  variables  as  functions  of  the 
heat  supplied  admit  in  their  interpretation  of  the  statement  of 
many  important  new  propositions.  Some  of  these  are  quite  gen- 
eral, while  others  are  more  specific.  A  few  of  the  most  obvious 
will  be  noted. 

The  cycle  consists  of  a  series  of  operation  or  pressure  volume 
temperature  changes  resulting  in  a  return  to  the  original  state  of 
pressure  volume  and  temperature. 

GENERAL  PROPOSITIONS. 

I.  The  P.V.T.  at  any  point  of  a  cycle  depends  on :  (a)  The  cycle 
itself  qualitatively  considered,  i.  e.y  the  nature  and  order  of  succession 
of  the  processes  or  phases  already  completed ;  (£)  the  extent  or 
intensity  of  each  phase  of  the  cycle  qualitatively ;  (c)  the  amount 
of  heat,  ff,  added  before  reaching  the  point  considered.  For  exam- 
ple, the  temperature  at  the  end  of  combustion  will  be  different  for 
different  cycles,  will  vary  with  the  compression  before  heating,  the 
law  of  compression  and  the  amount  of  heat  added. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  95 

2.  The  part  of  the  total  heat  transformed  into  work  is  a  function 
of  the  cycle,  and  will  vary  with  the  order,  nature  and  extent  of  the 
cyclic  phases,  except  when  all  the  heat  is  added  and  all  abstracted 
according  to  the  same  law. 

3.  When  the  laws  of  heating  and  of  cooling  are  identical  then 
the  part  of  the  total  heat  supplied  that  becomes  transformed  into 
work  is  constant  for  the  same  previous  compression,  and  this  re- 
sulting efficiency  is  a  function  of  the  previous  compression  only 
when  these  other  two  phases,  compression  and  expansion,  complet- 
ing the  cycle,  have  likewise  the  same  law. 

4.  The  range  of  changes  in  pressure  volume  and  temperature  is 
different  for  different  cycles,  and  in  any  one  cycle  will  depend  on 
the  amount  of  heat  added. 

5.  While  the  variations  noted  do  in  general  hold,  yet  in  the  dif- 
ferent cycles  each  variable  may  be  a  different  function  of  Hlt  so 
that  two  or  more  curves  may  intersect,  and  for  that  particular  value 
of  HI  the  variable  will  have  the  same  value  in  two  or  more  different 
cycles  simultaneously. 

EFFICIENCIES  (Fig.  52). 

By  inspection  and  plotting  of  formulae  Nos.  40-58,  page  90,  for 
the  values  of  heat  necessarily  discharged  we  may  draw  some  con- 
clusions concerning  efficiencies  of  the  transformation  process  for 
various  cycles.  Denoting  as  before  the  ratio  of  heat  energy  trans- 
formed to  that  supplied  by  E  =  efficiency,  it  will  be  possible  to 
draw  the  following  comparisons  : 

6.  For  Cycles  II.  A2,  III.,  IV.  C  the  efficiency  is  a  function  of 
the  adiabatic  compression  only  and  the  same  function  for  each. 
It  is  independent  of  the  amount  of  heat  supplied,  i.  e.,  is  not  a 
function  of  H. 

7.  For  all  cycles  the  efficiency  increases  with  the  compression, 
but  not  according  to  the  same  law. 

8.  For  Cycles  IV.,  IV.  A,  IV.  B,  IV.  C  the  efficiency  decreases 
with  increase  of  heat  added  to  the  same  mass  of  gas. 

9.  For  all  other  cycles  except  II.  A2,  III.,  IV.  C  the  efficiency 
increases  with  Hlt  but  according  to  different  laws,  so  that  the  dis- 
tance between  efficiency  curves  will  vary. 

10.  For  these  cases  a  change  in  Hl  will  produce  more  effect 
when  HI  is  small  than  when  it  is  large. 

11.  After  heat  has  been  added  the  efficiency  will  vary  with  the 


96  THE  HEAT  ENGINE  PROBLEM. 

degree  of  expansion.  Cycle  II..  therefore,  will  have  an  efficiency 
always  higher  than  II.  A  and  lower  than  II.  B  or  II.  C. 

12.  Cycles  in  which  an  adiabatic  compression  precedes  heating, 
will  always  have  a  higher  efficiency  than  those  lacking  this  com- 
pression, other  things  being  equal. 

I  3.  For  the  same  initial  conditions  and  same  heat  added  it  H^ 
is  large  enough  Cycle  II.  C  will  always  have  the  highest  efficiency 

(II.  A  ) 

and  then  come  in  order  III.  C;  I.  C;  II.    \  III.      >    always  re- 

I IV.  C  j 

membering  that  IV.,  IV.  A,  IV.  B,  IV.  C  cannot  exist  if  //a  be 
large. 

14.  The  difference  in  efficiency  between  the  curtailed  expansion 
of  Cycle  II.  A2  and  that  of  II.  increases  with  the  amount  of  heat, 
the  difference  being  small  when  H^  is  small  and  greater  as  Hv  in- 
creases, the  greatest  possible  being  about  12  per  cent. 

15.  Expanding  Cycle  II.  to  original  temperature  making  Cycle 
II.  C,  may  increase  the  efficiency  from  5  to  15  per  cent,  approxi- 
mately for  possible  values  of  //r 

1 6.  Cycle  III.  may  add  by  expansion  to  original  temperature  as 
much  as  25  per  cent,  to  the  efficiency  for  possible  values  of  H^ 

17.  Cycles  IV.,  IV.  A,  IV.  B  have  an  efficiency  decreasing  with 
increase  of  H  provided  H  remain  small ;  when  H  passes  a  certain 
limit  the  cycle  ceases  to  be  possible. 

1 8.  A  change  in  the  volume  ratio  of  compression  from  \  to  y1^ 
will  increase  the  efficiency  of  the  cycles  as  follows  for  possible 
values  of  H^. 

Cycle  II.    .    .    .    30-20  per  cent,  approximately,  depending  on  Hlt 

"  II-  A,  ) 

"  III.      r  •    •     35  Per  cent-  approximately,  depending  on  H 9 

«•  IV.  C  j 

"  II.  C   .    .     40-5  per  cent,  approximately,  depending  on  Hv 

TEMPERATURES  (Figs.  46,  49,  55). 

I.  For  the  same  previous  compression  the  temperature  resulting 
in  each  cycle  from  heat  addition  and  which  is  the  maximum  for 
the  cycle,  will  be  different.  That  is,  the  addition  of  the  same 
amount  of  heat  will  result  in  a  different  temperature  for  each  group 
of  cycles  and  the  lines  of  Fig.  46  show  that  no  two  can  be  iden- 
tical except  I.  and  III.,  which  cross. 


CYCLIC    ANALYSIS    OF    HEAT  ENGINES.  97 

2.  Gases  passing  through  Cycle  I.  may,  on  addition  of  a  certain 
amount  of  heat,  Hr  have  a  temperature  equal  to  what  the  same 
gas  would  have  passing  through  C>cle  III.     However,  for  more 
heat  added  the  temperature  for  I.  will  become  higher  than  that  for 
III.  while  for  less  heat  added  III.  will  be  higher. 

3.  Increase  of  compression  before  heating  changes  the  temper- 
ature after  heating  by  only  so  much   numerically  as   the  varied 
compression  has  resulted  in  changing  the  temperature  before  heat- 
ing begins. 

4.  The  temperature  increase  due  to  heating  is  proportional  to 
the  amount  of  heat  added  //lf  and  the  constant  of  proportionality 
involves  the  reciprocal  of  the  specific  heat  for  the  process  and  the 
weight  of  the  gas  present. 

5.  After  the  gas  has  expanded  to  the  greatest  volume  possible 
in  the  cycle,  no  two  cycles  will  leave  the  gas  with  the  same  tem- 
perature except  in  a  few  special  cases. 

6.  Cycle  I.  C,  II.  C,  III.  C,  IV.  C  by  definition  have  the  same 
temperatures  at  the  end  of  expansion,  and  this  is  moreover  con- 
stant no  matter  what  H  may  be  and  is  equal  to  the  initial  temper- 
ature of  the  cycle. 

7.  There  will  be  a  value  of  Hl  for  a  limited  range  of  compres- 
sions for  which  cycle  III.  may  give  to  the  gas  the  same  final  expan- 
sion temperature  as  Cycle  I. 

8.  Similarly  II.  for  one  compression  may  coincide  in  final  tem- 
perature with  II.  A  for  some  other  compression. 

9.  The  temperature  after  expansion  for  cycle  II.  A,  will  always 
be  higher  than  for  III.  and  III.  higher  than  for  II. 

10.  In  round  numbers  II.  A  may  be  25  per  cent,  higher  than  III. 
and  may  even  be  100  per  cent,  higher  than  II.  for  the  same  com- 
pression for  possible  values  of  ffr 

11.  With  variation  of  compression  the  temperature  at  the  termi- 
nation of  expansion  will  vary,  always  becoming    lower   but  the 
extent  of  the  lowering  will  depend  on  how  much  heat  was  added 
before  expansion  and  in  case  II.  A  and  III.  is  exactly  proportional 
to  Hr 

12.  A  change  of  compression  J  to  y1^  may  change  the  tempera- 
ture at  the  end  of  expansion  in  the  case  of  cycle  II.  A  and  III.  as 
much  as  80  per  cent,  for  possible  values  of  ffr 

1 3.  Mean  effective  temperature,  Fig.  55,  are  different  for  different 
cycles  and  for  different  compressions  in  the  same  cycle. 


9  THE  HEAT  ENGINE  PROBLEM. 

14.  Cycle  IV.  C  is  the  only  cycle  with  constant  mean  effective 
temperature. 

15.  Mean  effective  temperature  of  all  other  cycles  increase  with 
H, 

1 6.  For  large  values   of  H^  the  order  of  magnitude  of   mean 
effective  temperatures  will  be:  Lowest,  IV.  C,  III.  C,  I.  C,  II.  C, 
III.,  I.,  II.,  highest,  II.  A. 

17.  For  lower  values  of  Hl  this  order  may  be  somewhat  changed 
and  there  will  be  points  at  which  two  different  cycles  will  have 
simultaneous  values  of  M.E.T.  and  //r 

PRESSURES  (Figs.  47,  50,  53). 

1.  The  pressures  resulting  from  heat  addition  are  different  for 
cycles  with  different  numerals,  but  the  same  in  any  one  group. 
Thus,  II.,  II.  A,  II.  B,  II.  C  or  Group  II.  will  all  have  the  same 
pressures,  whereas    those  of   Group  II.  will  differ  from  those  of 
Groups  III.  and  IV. 

2.  Lines  representing  pressures  or  functions  of  the  heat  supplied, 
Hr  will  cross  as  these  functions  are  different  for  different  groups, 
and  it  will  hence  be  possible  for  the  different  groups  of  cycles  to 
have  the  same  pressures  for  certain  values  of  H^. 

3.  Groups  I.  and  II.  have  pressures  after  heating  that  increase 
with  H^  while  in  Group  III.  the  pressure  is  constant  and  in  IV. 
decreasing  with  increase  of  //r 

4.  For  same  compressions  Group  II.  will  always  have  the  high- 
est pressure  after  heating,  and  III.,  IV.  and  I.  come  in  the  order 
named  for  moderate  Hl%  while  for  large  Hl  IV.  cannot  exist. 

5.  Increase  of  compression  will  change  the  pressure  after  heat- 
ing in  Group  III.  only  so  much  as  results  from  the  changed  com- 
pression before  heating.     In  Groups  II.  and  I.  the  change  is  such 
as  to  keep  the  pressure  ratio  before  and  after  heating  constant ; 
so  that  for  a  given  change  in  Hl  the  resulting  pressure  change  in 
II.  will  be  greatest  for  high  compressions,  less  for  moderate  com- 
pressions and  least  for  no  compression,  i.  e.,  for  Group  I. 

6.  After  expansion  by  definition  the  pressures  of  I.,  II.,  III.  and 
IV.  are  all  atmospheric  and  equal. 

7.  The  pressure  which  II.  A2  will  reach  when  the  gas  has  ex- 
panded to  original  volume  increases  with  Hl  and  is  such  that  the 
ratio  of  this  pressure  to  atmospheric  is  the  same  as  the  ratio  of 
pressure  after  heating  to  that  before. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  99 

8.  Cycles  with  letter  Call  go  below  atmosphere  in  expanding  to 
such  a  pressure  as  will  bring  the  temperature  down  to  that  origi- 
nally existing  in  the  gas.     These  resulting  pressures  after  expan- 
sion are  different  for  each  cycle,  but  the  lines  representing  them  as 
functions  of  H^  may  intersect. 

9.  The  lines  for  IV.  C  may  cross  others,  but  I.  C,  II.  C,  III.  C 
cannot  intersect  and  these  will  always  be  in  the  order  of  magni- 
tude II.  C,  III.  C,  I.  C  and  all  asymptotic  to  axis  of  //,  so  that  the 
terminal  pressure  can  never  be  zero. 

10.  An  increase  of  compression  will  cause  an  increase  in  final 
pressure  for  same  //r 

11.  Mean  effective  pressure  expressed  as  a  function  of  Hl  will 
give  for  every  cycle  and  every  different  compression  a  different 
M.E.P.  curve,  but  as  before  these  may  intersect. 

12.  For  all  cycles  except  those  ending  with  isothermal  return 
to  the  original  state,  the  M.E.P.  increases  with  Hl  but  for  those 
bearing  the  letter  C  the  M.E.P.  decreases  and  for  no  cycle  is  it 
constant. 

13.  For  the  same  previous  compression  the  cycles  have  M.E.P. 
of  about   the   following   order  of   magnitude   when    Hl   is   large 
enough. 

Greatest  M.E.P.,  II.  A2,  200;  II.,  40;  I.,  25;  III.,  15;  II.  C, 
1.5;  I.  C,  0.3;  III.  C,  0.2.  When  H^  is  small  IV.  will  probably 
come  between  III.  and  II.  C, 

14.  A  change  in  compression  from  \  to  Tx¥  (vols.)  may  cause  a 
change  in  II.  A2  of  35  per  cent.,  II    of  100  per  cent.,  III.  of  300 
per  cent,  for  the  same  possible  values  of  Hr 

15.  The  effect  of  changed   compression  before  heating  is  the 
more  marked  on  M.E.P.  resulting  when  M.E.P.  is  lowest  and  the 
extent  of  the  increase  is  greater  with  H^ 

VOLUMES  (Figs.  48,  51,  54). 

1.  The  volumes  after  heating  are  the  same  for  cycles  of  the 
same  group  and  for  all  groups  increase  with  Hv  except  in  Groups 
I.  and  II.  where  by  definition  they  are  constant  and  equal  to  the 
volumes  existing  before  heating. 

2.  In  Group  III.  the  volumes  after  heating  are  proportional  to 
HI  with  the  same  constant  of  proportionality  for  the  same  com- 
pression.    Increase  of  compression  decreases  this  constant  of  pro- 
portionality. 


100  THE    HEAT    ENGINE    PROBLEM. 

3.  In  Group  IV.  the  volumes  increase  rapidly  with  Hv  but  are 
not  proportional  to  H^  so  long  as  H^  is  small ;  with  large  //,  Group 
IV.  cannot  exist. 

4.  Lines    of  volumes  after  heating  represented  as  functions  01 
Hl  may  cross  in  some  cases.     II.,  IV.  and  III.  may  cross  I., i.e., the 
compression  cycles  may  cross  the  non-compression  ones.     But  for 
the  same  compression  II.,  III.  and  IV.  can  never  have  the  same 
volumes  after  heating.     Lines  of  III.  and  IV.  for  high  compres- 
sion may  cross  II.  for  a  lower  compression  but  cannot  cross  each 
other. 

5.  For  possible  values  of  Hl  the  volumes  after  heating  for  the 
different  groups   may  have  the  following  order  of  magnitude  if 
//j  is  large  enough  :  Group  III.,  55.00;  group  I.,  12.38;  group  II., 
6.00. 

6.  After  expansion  is  completed  the  volume  occupied  by  the  gas 
in  the  different  cycles  will  vary  through  very  wide  limits,  increasing 
with  H^. 

7.  The  volume  occupied  by  Cycle  III.  will  be  such  as  to  keep 
the  ratio  between  this  final  volume  and  the  volume  before  com- 
pression the  same  as  the  ratio  ot  volume  after  heating  to  that  be- 
fore and  the  final  volume  is  proportional  to  Hv     The  constant  of 
proportionality  is  decreased  by  compression  increase. 

8.  The  final  volume  of  Cycle  II.  A  is  least  and  equal  to  that 
existing  before  compression. 

9.  When  H^  is  large  enough  there  may  be  a  value  for  which 
the  final  volume  may  exist  in  the  following  order  of  magnitude : 
III.  Clf  7,000.00;   I.  C,  4,200.00;  II.  C,  2,300.00;  III  ,  75.00;  I., 
65.00;  II.,  51.00,  II.  A2,   12.38.     A  change  of  compression   by 
which  the  volume  after  compression  is  one  fifth  that  for  the  pre- 
vious case  may  change  this  list  to  the  following  :  III.  C.,  1,000.00; 

I.  C,  4,200.00;    II.  C,  500.00;  III.,  40.00;  I.,  65.00;  II.,  34.00; 

II.  A2,  12.38. 

10.  The  mean  effective  volumes  increase  with  Hv  for  all  cycles 
except  II.  A2  in  which  this  variable  is  constant. 

11.  For  cycle  III.  the  M.E.V.  is  proportional  to  H^  and  increase 
of  compression  increases  the  constant  of  proportionality. 

From  the  data  here  set  down  the  selection  of  a  cycle  on  purely 
ideal  grounds  can  be  made  with  a  full  knowledge  of  all  the  con- 
ditions surrounding  the  selection  ;  that  is  knowing  what  results  are 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  IOI 

desired  the  cycle  that  theoretically,  ideally  or  mathematically  con- 
sidered gives  the  results  can  be  found  and  in  addition  it  is  easy  to 
see  what  accompanying  circumstances  are  inevitable.  If  that 
cycle  that  transforms  the  greatest  amount  of  heat  into  work  ideally 
is  wanted  it  is  readily  seen  that  II.  C  with  as  high  compression  as 
possible  must  be  selected,  but  it  is  also  evident  that  a  very  large 
volume  range  must  be  submitted  to.  If  that  cycle  with  the  lowest 
temperature  range  is  wanted  then  any  of  Group  IV.  must  be  taken. 

If  a  cycle  is  desired  that  will  convert  of  any  amount  of  heat  the 
same  proportion  into  work  then  any  one  of  II.  A,  III.  or  IV.  C, 
but  of  these  one  has  the  lowest  pressure  range,  another  the  lowest 
temperature  range  and  the  last  the  lowest  volume  range. 

Examples  could  be  multiplied  almost  indefinitely,  but  enough 
has  been  said  to  make  clear  the  purpose  of  and  justify  this  laborious 
analysis,  for  the  results  desired  can  be  set  down  at  once  for  cycles 
considered,  and,  moreover,  for  any  cycle  not  considered  it  is  evi- 
dent that  similar  treatment  will  place  it  at  once  in  comparison  with 
all  these  presented. 


NOTE. — This  paper  is  sent  to  you  that  you  may  examine  it  in  advance  of  the 
meeting,  and  prepare  any  discussion  of  it  which  you  may  wish  to  present. 
"  Tt  is  issued  to  the  membership  in  confidence,  and  with  the  distinct  understand- 
ing that  it  is  not  to  be  given  to  the  press  or  to  the  public  until  after  it  has  been 
presented  at  the  meeting. 

The  Society  as  a  body  is  not  responsible  for  the  statements  of  fact  or  opinion 
advanced  in  papers  or  discussion.  (Art.  44  of  its  Rules.) 

As  there  will  be  no  adequate  supply  of  extra  copies,  and  papers  are  liable  to 
be  read  by  abstract  only,  preserve  this  copy  for  your  use,  and 

BRING  THIS   COPY  WITH  YOU  TO  THE   MEETING. 

(Subject  to  Revision.) 

No.   926.* 

THE  HEAT-ENGINE  PROBLEM.  \ 

BY   CHARLES   E.    LUCRE,    NEW   YORK. 

(Non-Member.) 

*  AND  PRESENTED  BY  R.  H.  FERNALD. 

(Associate  Member.) 

1.  A  MATHEMATICAL  analysis  of  the  different  cycles  of  variation 
of  state  through  which  a  mass  of  gas  may  pass  can  give  no  more 
than  a  provisional  idea  of  the  value  of  those  cycles  for  convert- 
ing the  energy  of  heat  into  useful  power.  Such  an  analysis 
must  presuppose  certain  ideal  conditions  that  may  or  may  not 
be  possible  in  practice,  and  though  mathematically  we  may  find 
that  one  cycle  should  convert  more  of  the  heat  supplied  into  work 
than  any  other,  there  may  be  difficulties  in  the  way  of  practically 
getting  this  result.  It  may  happen,  for  example,  that  a  very 
complicated  large  or  heavy  machine  is  necessary,  or  that  the 

*  To  be  presented  atlhe  New  York  meeting  (December,  1901)  of  the  American 

Society  of  Mechanical  Engineers,   and  forming  part  of  Volume  XXIII.  of  the 

Transactions. 
f  For   further  discussion   on   the    same    topic    consult   the    Transactions  as 

follows  : 

No.  843,  vol   xxi.,  p.  396  :  "An  Efficiency  Test  of  a  One  Hundred  and  Twenty- 
five  Horse-power  Gas  Engine."     C.  H.  Robertson. 

No.  861,  vol.  xxi.,  p.  961  :    "The  Gas-engine  Hot  Tube  as  an  Ignition-timing 
Device."     Win.  T.  Magruder. 

No.  875,  vol.  xxii.,  p.  152  :  '"  Efficiency  of  a  Gas  Engine  as  Modified  by  Point  of 
Ignition."     C.  V.  Kerr. 

No.  879,  vol.  xxii.,  p.  312:  "A  New  Principle  in  Gas-engine  Design,"     C.  E. 
Sargent. 

No.  895,  vol.  xxii.,  p.  612  :  "  Efficiency  Tests  of  a  One  Hundred  and  Twenty-five 
Horse-power  Gas  Engine."     C.  H.  Robertson. 


2  THE  HEAT-ENGINE  PROBLEM. 

required  changes  of  state  in  the  gas  cannot  be  carried  out  at 
all,  or,  perhaps,  not  fast  enough  to  be  useful  in  a  prime  mover. 
In  the  general  study,  then,  of  the  heat-engine  problem,  we 
must  add  to  the  analytic  cyclic  discussion  a  careful  considera- 
tion of  a  number  of  practical  questions,  the  results  of  which, 
when  allied  with  the  mathematical  analysis,  will  permit  of  a 
logical  selection  of  the  proper  cycle  to  which  we  should  devote 
our  executive  energies  ;  their  goal  is  the  production  of  that 
prime  mover  whose  source  of  energy  shall  be  heat,  whose 
medium  of  transformation  of  this  heat  into  work  a  perfect  gas, 
and  which  shall  call  for  the  simplest  machine,  giving  the  greatest 
power  in  the  smallest  space  with  the  least  metal  and  under  the 
most  favorable  circumstances. 

2.  Every  cycle  available  for  transforming  heat  energy  into 
mechanical  energy  by  the  moving  of  a  part  against  a  resistance, 
must  include  as  one  of  its  phases  the  heating  of  the  gas  in  some 
particular   way  peculiar  to  that  cycle.      This  giving  of  heat 
energy  to  the  transforming  gas  presupposes  a  source  of  heat 
which  in  practice  must  be  a  fire.     The  heat  of  a  fire  may  be 
imparted  to  a  mass  of  gas  in  three  ways  : 

I.  The  fire  may  be  placed  on  one  side  of  a  wall  through  which 
the  heat  must  pass  to  the  mass  of  gas  on  the  other  side ;  this 
may  be  termed  external  heating. 

II.  The  fire  may  be   caused  to  heat  a  solid  mass,  which  is 
afterward  shut  off  from  the  fire  and  brought  into  contact  with 
the  mass  of  gas ;  this  is  a  combination  of  external  and  internal 
heating. 

III.  The  fire  may  be  enclosed  and  maintained  by  the  mass  of 
gas  itself ;  in  this  case  the  gas  must  be,  at  least  in  part,  air  which 
will  furnish  oxygen  for  this  internal  combustion. 

3.  Any  system  which  depends  on  the  heating  of  the  gas  by 
contact  with  solid  matter  at  a  high  temperature,  must  necessarily 
be  slow  in  operation  and  involve  large  masses  of  gas.     For  the 
transfer  of  heat,  the  source   must  be  hotter  than  the  receiving 
mass,  and  a  difference  of  temperature,  for  a  given  rate  of  transfer 
sufficiently  high  to  be  of  practical  value,  must  be  greater  than 
the  medium  of  transfer  can  stand  without  injury.     Consider 
how  hot  the  walls  of  a  chamber  would  have  to  be  to  heat  a  mass 
of  gas  as  rapidly  as  is  done  in  the  gas  engine,  and  the  point 
made  above  will  be  clear.     Nevertheless,  engines  with  this  kind 
of  heating  have  been  built,  but,  admirable  as  some  of  them  have 


THE   HEAT-ENGINE  PROBLEM.  6 

been  in  conception,  they  bave  proved  failures  as  prime  movers 
in  competition  with  others  because  of  the  points  noted.  The 
engines  of  Ericsson,  Eankine,  and  the  Stirlings  are  all  in- 
cluded in  this  class,  with  results  that  are  well  known.  Erics- 
son's large  engine  of  300  horse-power  showed  a  mean  effective 
pressure  of  about  2  pounds  per  square  inch  with  a  piston  area 
of  600  square  feet.  The  only  machine  now  working  with  this 
external  heating  is  the  one  known  as  Eider-Ericsson,  used  in 
small  sizes  only  for  the  slow  pumping  of  water. 

4.  Nothing  that  this  system  can  do  will  compare  with  what 
may  be  derived  from  the  use  of  the  internal-combustion  method 
of  heating.     This  internal-combustion  heating  of  a  mass  of  gas 
will  permit  of  a  heating  as  rapid  as  we  choose,  and  to   any 
temperature  up  to  a   certain   maximum.     If  all  the   air   sup- 
plied has  its  oxygen  converted  with  the  fuel  to  CO2,  H^O,  etc., 
there  being  no  excess  of  either  oxygen  or  fuel,  then  the  mass  of 
gas  which,  it  is  true,  has  changed  in  chemical  composition,  but 
not  materially  in  physical  properties,  has  received  the  maxi- 
mum amount  of  heat  obtainable   from  the   combustion  of  the 
fuel  used.    If  only  a  part  of  the  air  support  combustion  and  the 
products  be  diluted  with  unused  air  or  by  steam,  etc.,  then  any 
desired  temperature  between  the  original  temperature  of  the 
gases  and  the  maximum  may  be  obtained.     The    problem  of 
heating  gases  by  an  internally  maintained  fire  is  difficult,  com- 
pared with  the  other  method  of  external  heating,  and  this  may 
account  for  its  later  application.     We  might  say  in  brief  that 
externally   heating   a   gas   is   thermally   bad  but  easily  done, 
internally   heating   the   gas,   thermally   good  but  not  so  easy 
to  do. 

5.  Heating  working  gases  by  internal  combustion  has  been 
done  with  coal,  oil,  and  gas.     The  methods  used  might  be  tabu- 
lated briefly. 

I.  With  coal : 

(a)  Air  is  passed  through  a  coal  fire  with  or  without  a  grate. 
Cayley,  Shaw,  and  Genty. 

(6)  A  coal  fire  is  moved  through  an  enclosed  mass  of  air. 
Lord. 

II.  With  liquid  fuel  not  previously  vaporized  : 

(a)  The  enclosed  air  acts  as  a  quiet  atmosphere  supporting 
the  combustion  of  a  jet  of  oil  flame.     Diesel. 

(b)  The  air  is  caused  to  move  past  a  burner,  and  in  passing 


THE    HEAT-ENGINE   PROBLEM. 

supports  combustion,  the  heated  products  passing  on.  Wilcox, 
Bray  ton,  Nordberg,  and  Shad  all. 

(c)  Oil  is  thrown  into  a  hot  chamber,  there  vaporized,  and 
brought  into  contact  with  the  air,  the  proportions  being  so 
maintained  as  to  make  the  resulting  gaseous  mixture  explosive. 
Combustion  is  of  the  self- propagated  sort.  Hornsby,  Mietz  & 
Weiss,  and  Capitaine. 

III.  With  gas  or  previously  vaporized  oil : 

(a)  An  enclosed  air  atmosphere  supports  a  quiet  jet  of  gas 
flame.     Diesel  and  Gibbs. 

(b)  Air  in  motion  passes  a  fixed  gas  flame  as  in  most  atmos- 
pheric engines.     Wilcox,  Weiss,  and  Otto  atmospheric. 

(c)  Air  mixed  with  gas  in  explosive  proportions  is  caused 
to  pass  a  point  where  the  combustion  is  localized.     Brayton, 
Schmid,  Beckfeld,  and  Reeve. 

(d)  Air  mixed  with  gas  in  explosive  proportions  is  enclosed 
in  a  chamber,  and  while  at  rest  burned  by  self-propagation, 
after  inflammation  was  provoked   by  a   local  ignition.     Otto, 
Priestman,  Nash,  Westinghouse,  and  in  fact  nearly  all  existing 
internal-combustion  engines. 

The  above  classification  leads  directly  to  the  broad  division 
of  internal-combustion  engines  into  two  great  classes,  the  explo- 
sive and  non-explosive.  The  term  "  explosive  "  we  shall  apply  to 
all  those  engines  in  which  a  mass  of  gaseous  mixture  at  rest  is 
ignited  at  one  point,  and  the  whole  burned  by  self-propagation. 
The  other  term, "  non-explosive,"  we  shall  apply  to  those  engines 
in  which  the  gases  are  in  motion  and  in  that  motion  pass  a 
point  where  combustion  is  localized,  and  are  there  heated  in  the 
passing.  To  complete  our  terminology,  we  add  the  expressions 
"  intermittent  non-explosive,"  to  those  machines  in  which  the 
combustion  is  periodically  interrupted  at  the  cylinder  end  as 
in  Diesel's,  and  "  continuous  non-explosive  "  to  those  in  which 
the  combustion  is  maintained  in  a  chamber,  and  the  hot  gases 
used  as  required,  as  in  Reeves,  Schmid,  and  Beckfeld. 

We  have,  then,  explosive  engines  ;  non-explosive  engines  with 
intermittent  combustion,  or  continuous  combustion  as  the  dif- 
ferent kinds  of  internal-combustion  engines. 

6.  The  explosive  engine  as  developed  and  perfected,  chiefly 
by  Dr.  Otto,  holds  the  field  to-day,  and  its  very  general  use 
has  brought  out  its  merits  and  demerits.  It  has  been,  and  is 
to-day,  the  subject  of  many  researches  and  experiments,  all 


THE   HEAT-ENGINE   PROBLEM.  5 

tending  to  perfect  it  by  the  discovery  of  its  faults.  All  this  has 
resulted  in  its  present  position,  which  might  be  summed  up  as 
follows  : 

It  is  extremely  simple  in  construction,  having  comparatively 
few  working  parts.  . 

The  thermal  changes  of  heating  and  expansion  are  all  per- 
formed in  the  same  place,  on  a  quiet  mass  of  gas,  and  nothing 
but  the  gas  is  heated. 

The  best  engines — those  of  rational  design — do  not  differ  much 
in  construction  and  results,  and  this  brings  out  an  important 
point — that  in  the  handling  of  a  mass  of  gas  to  be  exploded,  we 
accept  a  certain  inflexibility  from  which  we  cannot  escape. 

7.  As  a  machine,  it  cannot  compare  with  the  steam  engine. 
It  is  not  easy  to  start,  and  cannot  be  worked  at  widely  variable 
speeds ;  its  governing  is  bad,  the  speed  varying  at  different  points 
of  the  stroke,  but  adding  up  to  a  fairly  constant  total  number  of 
revolutions  per  minute  ;  it  has  no  margin  of  power  and  carries 
an  ignition  system  that  once  deranged  stops  the  machine  ;  it  is 
non-reversible ;  it  has  a  low  mean  effective  pressure  for  high- 
pressure  range,  hence  is  heavy ;  it  can  use  only  one  kind  of 
fuel,  and  that  gas,  and  whether  this  be  produced  from  oil  or 
coal,  it  must,  nevertheless,  be  produced  outside  the  natural  gas 
regions.     It  cannot,  and  never  will  be,  able  to  use  crude,  unre- 
fined oils  directly ;  it  operates  under  only  one  fixed  cycle. 

8.  About  as  much  can  be  said  for  the  explosive  type  as  against 
it.     It  has  occupied  nearly  all  workers  in  the  internal-combus- 
tion field  for  the  past  thirty  years,  and  the  success  attained 
continues  to  draw  to  the  problem  large  numbers  of  men  and 
an  immense  amount  of  capital,  and  these,  working  together, 
must  do  much  for  this  type  in  the  future.     But  while  this  good 
work  goes  on,  there  is  no  reason  why  the  other  types  of  internal- 
combustion  engines  should  not  receive  their  share  of  attention. 
Some  have  been  built  and  many  proposed;  some  were  successful 
and  some  failures ;  but  a  careful  study  of  what  has  been  done 
successfully  and  the  cause  of  failure  of  the  unsuccessful  en- 
gines would,  if  no  more,  show  clearly  the  possibilities  of  this  type. 
If  the  difficulties  are  clearly  set  forth,  the  solution  will  be  the 
easier,  and  if  in  the  study  of  the  difficulties  the  solution  appears, 
so  much  the  better. 

Of  the  successful  engines  of   the  non-explosive  type,  there 
may  be  mentioned  two  that  easily  head  the  list,  the  old  Bray- 


THE   HEAT-ENGINE   PROBLEM. 


ton  and  the  modern  Diesel,  and  the  results  obtained  from  these 
machines  are  certainly  encouraging.  However,  before  entering 
into  a  discussion  of  the  various  non-explosive  machines,  it  would 
be  well  to  make  sure  of  our  theoretical  grounds. 

9.  The  different  cycles  of  operation  that  might  be  performed 
on  a  mass  of  gas  are  infinite/ but  there  is  a  limited  number  which 
are  striking  and  simple.  These  are  given  below. 

Let  Fig.  1  be  a  pressure-volume  diagram  for  the  Cycle  I. 

Then  we  have  : 

From  B  to  (7.  Addition  of  heat  isometrically  from  atmos- 
pheric pressure. 

From  C  to  D.     Adiabatic  expansion  to  atmospheric  pressure. 

From  D  to  B.     Cooling  at  atmospheric  pressure. 
P  CYCLE.  I 


•D. 


v 


FIG.  1. 


In  Fig.  2  we  have  for  Cycle  IA.: 

From  B  to  (7.     Addition  of   heat  isometrically   from   atmos- 
pheric pressure. 

CYCLE  I  A. 


FIG.  2. 


THE   HEAT-ENGINE  PBOBLEM. 


From  C  to  D.  Adiabatic  expansion  to  a  point  above  atmos- 
pheric pressure. 

From  D  to  E.     Cooling  isometrically  to  atmospheric  pressure. 

From  E  to  E.     Cooling  at  atmospheric  pressure. 

In  Fig.  3  we  have  for  Cycle  IB.: 

From  B  to  C.  Addition  of  heat  isometrically  from  atmos- 
pheric pressure. 

From  C  to  D.  Adiabatic  expansion  to  below  atmospheric 
pressure. 

From  D  to  E. 

From  E  to  B. 


Cooling  isothermally  to  atmospheric  pressure. 
Cooling  at  atmospheric  pressure. 


CYCLE  I.B. 


V. 


FIG.  3. 


In  Fig.  4  we  have  for  Cycle  1C.: 

From  B  to  C.     Addition  of  heat  isothermally  from   atmos- 
pheric pressure. 


CYCLE  1C 


V 


FIG.  4 


8 


THE   HEAT-ENGINE   PROBLEM. 


From  C  to  D.  Adiabatic  expansion  to  a  pressure  below 
atmospheric  such  that  we  get, 

From  D  to  B.  Cooling  isothermally  to  the  original  volume 
and  atmospheric  pressure. 

In  Fig.  5  we  have  for  Cycle  II : 

From  A  to  B.  Adiabatic  compression  from  atmospheric 
pressure. 

From  B  to  C.     Addition  of  heat  isometrically. 

From  C  to  D.     Adiabatic  expansion  to  atmospheric  pressure. 

From  D  to  A.     Cooling  at  atmospheric  pressure. 


CYCLE  II 


FIG.  5. 


In  Fig.  6  we  have  for  Cycle  TLA.: 

From  A   to   B.     Adiabatic   compression   from   atmospheric 
pressure. 
From  B  to  C.     Addition  of  heat  isometrically. 


CYCLE  HA. 


FIG.  6. 


THE   HEAT-ENGINE  PROBLEM. 


From   C  to  D.     Adiabatic   expansion   to   a   pressure  above 
atmospheric. 

From  D  to  E.    Cooling  isometrically  to  atmospheric  pressure. 
From  ^to  A.     Cooling  at  atmospheric  pressure. 
In  Fig.  7  we  have  for  Cycle  IIB.: 

From   A    to   B.     Adiabatic   compression   from   atmospheric 
pressure. 

Addition  of  heat  isometrically. 

Adiabatic  expansion  to  pressure  below  atmos- 


From  B  to  C. 
From  C  to  D. 
pheric. 

From  D  to  E. 
From  Eio  A. 


Cooling  isothermally  to  atmospheric  pressure. 
Cooling  at  atmospheric  pressure. 


CYCLE  KB. 


A. 


V 


FIG.  7. 


In  Fig.  8  we  have  for  Cycle  11(7.: 

From  A  to  B.     Adiabatic  compression  from  atmospheric  pres- 
sure. 

CYCLE  JIG 


V 


FIG.  8. 


10 


THE   HEAT-ENGINE   PROBLEM. 


From  B  to  C.     Addition  of  heat  isometrically. 

From  C  to  D.  Adiabatic  expansion  to  a  pressure  below 
atmospheric  such  that  we  get, 

From  D  to  A.  Cooling  isothermally  to  the  original  volume 
and  atmospheric  pressure. 

In  Fig.  9  we  have  for  Cycle  III : 

From  A  to  B.  Adiabatic  compression  from  atmospheric 
pressure. 

From  B  to  0.     Addition  of  heat  isopiestically. 

From  G  to  D.     Adiabatic  expansion  to  atmospheric  pressure. 

From  D  to  A.     Cooling  at  atmospheric  pressure. 

CYCLE  111 


FIG.  9. 


In  Fig.  10  we  have  for  Cycle 

From  A  to  B.  Adiabatic  compression  from  atmospheric 
pressure. 

From  B  to  C.     Addition  of  heat  isopiestically. 

From  G  to  D.  Adiabatic  expansion  to  a  pressure  above 
atmospheric. 

P  CYCLEIA. 


FIG.  10. 


THE   HEAT-ENGINE   PROBLEM. 


11 


From  D  to  E.     Cooling  iso metrically  to  atmospheric  pressure. 

From  E  to  A.     Cooling  at  atmospheric  pressure. 

In  Fig.  11  we  have  for  Cycle  Illi?.: 

From  A  to  B.  Adiabatic  compression  from  atmospheric 
pressure. 

From  B  to  C.     Addition  of  heat  isopiestically. 

From  C  to  D.  Adiabatic  expansion  to  a  pressure  below 
atmospheric. 

From  D  to  E.     Cooling  isothermally  to  atmospheric  pressure. 

From  E  to  A.     Cooling  at  atmospheric  pressure. 

CYCLE    fflli 


FIG.  11. 

In  Fig.  12  we  have  for  Cycle  III6Y.: 

From  A  to  B.  Adiabatic  compression  from  atmospheric 
pressure. 

From  B  to  C.     Addition  of  heat  isopiestically. 

From  C  to  D.  Adiabatic  expansion  to  a  pressure  below 
atmospheric  such  that  we  get, 


p 


CYCLE   111C. 


A. 


V  -    » 


FIG.  12. 


12 


THE   HEAT-ENGINE   PROBLEM. 


From  D  to  A.     Cooling  isothermally  to  the  original  volume 
and  atmospheric  pressure. 

In  Fig.  13  we  have  for  Cycle  IV.: 

From   A   to  B.     Adiabatic   compression   from    atmospheric 
pressure. 

Addition  of  heat  isothermally. 

Adiabatic  expansion  to  atmospheric  pressure. 

Cooling  at  atmospheric  pressure. 


CYCLE   IV. 


From  B  to  C. 
From  C  to  D. 
From  Eto  A. 


FIG.  13. 


In  Fig.  14  we  have  for  Cycle  IV  A.: 

From   A    to  B.     Adiabatic   compression    from   atmospheric 


pressure. 


a  CYCLE    IVA. 


FIG.  14. 


THE   HEAT-ENGINE   PROBLEM. 


13 


From  B  to  G.     Addition  of  heat  isothermally. 

From  G  to  D.  Adiabatic  expansion  to  a  pressure  above 
atmospheric. 

From  I)  to  E.     Cooling  isometrically  to  atmospheric  pressure. 

From  E  io  A.     Cooling  at  atmospheric  pressure. 

In  Fig.  15  we  have  for  Cycle  IV B.: 

From  A  to  B.  Adiabatic  compression  from  atmospheric 
pressure. 

From  B  to  G.     Addition  of  heat  isothermally. 

From  G  to  D.  Adiabatic  expansion  to  a  pressure  below 
atmospheric. 

From  D  to  E.     Cooling  isothermally  to  atmospheric  pressure. 

From  E  to  A.     Cooling  at  atmospheric  pressure. 


P    iB 


CYCLE   IV B 


A. 


FIG.  15. 

In  Fig.  16  we  have  for  Cycle  IV C.: 

From  A  to  B.  Adiabatic  compression  from  atmospheric 
pressure. 

From  B  to  C.     Addition  of  heat  isothermally. 

From  G  to  D.  Adiabatic  expansion  to  a  pressure  below 
atmospheric  such  that  we  get, 

From  D  to  A.  Cooling  isothermally  to  the  original  volume 
and  atmospheric  pressure. 

Besides  these  there  are  various  atmospheric  cycles — some- 
times called  vacuum  cycles — in  which  the  first  step  is  the  heat- 
ing of  the  entering  charge  at  atmospheric  pressure.  Because 
of  their  slight  importance  they  are  here  omitted. 


THE   HEAT-ENGINE    PROBLEM. 


CYCLE  JVC. 


A. 


FIG.  16. 

10.  A  very  careful  mathematical  analysis*  of  all  these  cycles 
leads  to  these  conclusions  : 

(A)  Cycle  I.  and  its  variations,  by  reason  of  its  poor  showing 
in  efficiency  and  mean  effective  pressure  as  compared  with  the 
previous-compression  Cycle  II.,  must  be  set  aside. 

(B)  The  atmospheric  cycles,  by  reason  of  their  low  mean 
effective  pressure  and  consequent  large  volume  range,  are  use- 
less for  power  purposes  as  compared  with  the  other  cycles. 

(C)  This  leaves  as  the  only  cycles  worthy  of  application,  II., 
III.,  IV.,  and  their  variations. 

(D)  Of  the  last  mentioned,  there  are  three  which  are  peculiar, 
and  these  are  :  Cycle  11,4.,  Otto,  heating  and  cooling  the  gas 
at  constant  volume ;  Cycle  III.,  Brayton,  heating  and  cooling 
the  gas  at  constant  pressure,  and  Cycle  IV  (7.,  Carnot,  heating 
and  cooling  the  gas  at  constant  temperature. 

All  these  have  the  same  efficiency  for  the  same  compression, 
and  should,  consequently,  with  the  same  heat  supplied,  do  the 
same  work. 

The  efficiency  of  each  is  given  by 


where   Va  is  the  volume  before  compression, 
F6      "  "        after  £i 

;/       "        ratio  of  specific  heats,  and  for  air,  y  ~  1.406. 
*  Columbia  School  of  Mines  Quarterly,  Nos.  1,  2,  3,  vol.  xxii.,  1901. 


THE   HEAT-ENGINE  PROBLEM.  15 

(E)  The  other  cyclos,  II.,  IIB.  and  C.;   Ill  A.  and  B.;  IV., 
IV A.  and  B.,  can  easily  be  given   their   proper  comparative 
position  by  remembering  that  each  is  a  more  or  less  complete 
expansion  of  one  of  the  above  three.     For  example,  if  in  the 
Otto  the  expansion  were  carried  to  atmospheric  pressure,  the 
efficiency  would  be  greater  than  for  the  Otto.     Similarly  with 
the  Carnot,  if  the  expansion  were  stopped  at  atmospheric  pres- 
sure as  was  first  suggested  by  Diesel,  the  resulting  Cycle  IV. 
would  have  an  efficiency  less  than  the  Carnot,  and  hence  less 
than  either  the  Otto  or  Brayton  cycles. 

(F)  The  other  variables  entering  have  the  values  tabulated 
for  each  of  the  cycles  adopted  for  comparison. 

(  Same  mass  of  gas, 
Given  the  •<  Same  heat  supplied  after, 
'  Same  compression. 

There  will  result  for 

Cycle    II A.,  Otto        } 

"     III.       Brayton  >•  Same  work  done,  and  lience  same  efficiency. 
"      IV  C.     Carnot    ) 

And,  further, 

Lowest.  Intermediate.  Highest. 

Maximum  temperature Carnot  Brayton  Otto 

Pressure  range Brayton  Carnot  Otto 

Volume  range   Otto  Brayton  Carnot 

Temperature  range Carnot  Brayton  Otto 

Mean  effective  pressure Carnot  Brayton  Otto 

Pressure  range 

;rj ~ — T^ —  -  •  •  •  •    Brayton  Carnot  Otto 

Mean  effective  pressure 

Mean  effective  temperature Carnot  ayton  Otto 

The  relation  of  the  Diesel  to  the  Otto  an  Brayton  is  easily 
seen,  if  we  remember  it  as  an  imperfect  Car..ot. 

11.  Some  of  these  variables  should  be  a  maximum  and  some 
a  minimum.  For  the  maximum  teii*~  crature  the  Carnot  holds 
first  place,  but  its  impracticability  yields  the  place  to  Brayton. 
Neither  pressure  range  nor  mean  effective  pressure  is  wanted 
by  itself,  but  only  the  ratio  between  them,  for  it  is  to  this  ratio 
that  the  weight  of  the  engine  must  be  approximately  propor- 
tional ;  here  Brayton  holds  the  most  favorable  place. 

Volume  range  should  be  low,  and  here  first  place  is  held  by 
the  Otto.  The  mean  effective  temperature  should  be  low,  and 
the  Brayton  is  exceeded  only  by  the  Carnot. 

The  low  mean  effective  pressure  of  the  Carnot,  and  all  other 


16  THE  HEAT-ENGINE  PKOBLEM. 

isothermal  combustion  cycles,  is  sufficient  warrant  for  cutting 
them  out  of  consideration  in  comparison  with  the  Cycles  II., 
III.,  and  their  variations. 

We  have  thus  arrived  at  the  conclusion  that,  theoretically, 
the  last-named  cycles  only  are  worthy  of  further  consideration. 

Of  these  the  Brayton,  III.,  holds  a  most  favorable  position, 
being  surpassed  by  the  Otto  only  in  the  position  of  volume 
range. 

12.  In  the  above,  the  hypothesis  that  heat  could  be  added  to 
the  gas  has  been  assumed,  and  no  account  taken  of  the  means 
of  so  doing,  but   this   point  needs  consideration.     If  heat  be 
added  through  walls  from  a  source  of  known  supply,  of  which 
we    can    control   and   use  as   much  or  as  little  as  we  please, 
there  will  be  no  alteration  in  the   formulae  or  results  of  the 
analytical  comparison;  but  the  internal- combustion  method  of 
heating  presents  some  new  questions  for  solution.    First,  the  air 
and  fuel  become  carbonic  acid,  steam,  etc.,  and  as  to  what  value 
of  the  specific  heat  should  be  used,  who  can  say  ?     Second,  the 
chemical  change  is  accompanied  by  an  intrinsic  volume  change. 
Third,  there  may  be  reasons  why  the  fuel  should  give  out  more 
heat  when  burned  in  one  way  than  when  burned  in  another. 

13.  The  only  ways  of  heating  by  internal  combustion  that  are 
worth  anything  for  power  are  the  constant  volume  and  constant- 
pressure  methods.     On  theoretical  grounds,  we  have  no  reason 
for  saying  that,  for  any  particular  system  of  combustion,  more 
heat  can  be  developed  one  way  than  the   other.     The  evidence 
that  heat  has  been  added  to  a  mass  of  gas  in  an  engine  is,  for 
the  two  cases  :  (A)  an  increase  of  pressure,  and  (B)  an  increase 
of  volume.     This  pressure  increase  on  the  one  hand  and  vol- 
ume increase  on  the  other  we  can  readily  observe  by  indicators, 
and  the  results  of  these   observations  on  a  large  number  of 
indicator  cards  show  that  the  increase  is  not  what  it  should 
be  if  all  the  calorific  value  of  the  fuel  had  developed. 

In  short,  there  is  in  practice  abundant  evidence  of  heat  supres- 
sion,  and  whether  this  be  due  to  radiation,  conduction,  dissocia- 
tion or  an  increase  of  specific  heat,  or  to  an  actual  non-production 
of  heat  is  unknown.  What  we  do  know  and  can  assert  is  that  the 
effects  on  pressure  and  volume  are  such  as  they  would  be  if 
only  a  part  of  the  heat  supposed  to  be  generated  had  appeared. 
The  result  might  be  worked  up  to  give  a  new  value  to  the  heat- 
ing power  of  the  fuel,  to  be  called  its  effective  calorific  value,  or  a 


THE   HEAT-ENGINE   PROBLEM. 


new  value  given  to  the  specific  heat,  to  be   called  the  effective 
specific  heat  of  the  process. 

14.  For    constant-volume    combustion  we    have,   for   H},  the 
British  thermal  units  per  pound  of  mixture, 


where  pl  =  pressure  before  compression. 

Tl  —  temperature  before  combustion. 
p2  •=.  pressure  after  combustion. 
T.2  =  temperature  after  combustion. 
Cv  =  specific  heat  at  constant  volume. 

This  ratio  in  the  general  run  of  gas  engines  will  average 
about  3.5,  In  some  cases  it  may  reach  4,  but  I  know  of  no  case 
where  it  has  reached  5.  Some  values  are  given  below: 

J92 

Engine.  pl  Remarks. 

Westingliouse 3      On  Gas 

Otto 4.5  N.Y.Gas 

Hornsby  Ackroyd 3.5  Kerosene 

Nash 4      ....N.Y.Gas 

Clerk 4      Glasgow  Gas 

Crossley 3      Dowson  Gas 

f  Priestman 3.5  Kerosene 

Crossley  oil 3.5  .* Kerosene 

A  general  statement,  very  nearly  true,  would  give  these  pres- 
sure and  temperature  ratios  about  50  per  cent,  of  what  the  usual 
values  of  II{  and  Cv  would  produce.  These  figures,  while  not 
strictly  true  for  any  one  case,  give  a  fair  average  value. 

15.  The  other  system  of  combustion — that  at  constant  pres- 
sure— may  be  observed  in  the  same  way.  The  only  indicator 
card  I  have  of  this  type  of  engine  was  taken  from  a  Brayton  oil 
engine  with  its  smoky  fire.  The  volume  ratio,  in  this  case,  is 
quite  well  given  by  the  relative  lengths  of  the  delivery  line  of 
the  compressor  and  the  admission  line  of  the  power  cylinder, 
and  is  given  by 

?  =  3-2. 

Let  us  see  how  this  compares  with  the  pressure  ratios  given. 
Theoretically, 

*  =  -?"« -i  +  L?L 

91   ~     V    ~  f^    '7T  ' 


18  THE   HEAT-ENGINE  PROBLEM. 

where  Cp  is  the  specific  heat  at  constant  pressure  and  the 
other  symbols  are  as  heretofore  ;  combining  this  with  the  simi- 
lar one  for  the  other  type  we  get 


or 


' 

V 


=  1  +  y     ~  -  1  Take  y  =  1.4  ;  and 


By  substitution,  when 

l?2=l,     we  get 


'2  9  «  «  *  9    A 

=  &.  —  —  as±, 

V,  Pi 

^-  =  3,  "      "      ^-  =  3.8. 

Vl  Pi 

-^-  =  3.2,  "      "      ^-  =  444. 


16.  This  shows  thai  when  a  Brayton  engine  gives  a  volume 
ratio  in  combustion  of  3.2,  there  is  evidence  of  as  much  heat  as 
would  cause  a  pressure  ratio  of  4.44  in  an  explosion  engine  ; 
hence  it  would  seem  that,  for  the  combustion  process  alone,  the 
Brayton  engine,  even  with  its  poor  fire,  was  giving  evidence  of 
as  much  heat  as  the  very  best  explosion  engine,  and  more  than 
can  most  of  them.     This  point  is  very  striking,  and,  in  order  to 
verify  or  disprove  it,  a  large  mass  of  data  is  necessary,  which 
can  be  collected  only  after  considerable  time. 

The  above  point  bears  strongly  on  the  formulae  of  cyclic  com- 
parison. The  analysis  showed  that  the  Otto  and  Brayton  cycles 
must  have  the  same  efficiency  for  the  same  heat  added  ;  but,  if 
one,  by  reason  of  its  system  of  combustion,  can  take  from  the 
fuel  more  heat  than  the  other,  then  that  one  must  have  the 
higher  efficiency. 

17.  All  non-explosive  internal-combustion  engines,  except  the 
atmospheric  types,  must  provide  for  three  stages  :  first,  the  sup- 
plying of  working  gases,  which  are  derived  from  air  and  fuel, 
hence,  we  need  an  air  and  a  fuel  supply  ;  second,  the  causing  of 


THE   HEAT-ENGINE   PROBLEM.  19 

the  combination  of  the  fuel  and  air  in  combustion  to  raise  their 
temperature,  and  thereby  vary  either  pressure  or  volume  of  the 
gas,  as  we  desire ;  third,  the  utilization  of  the  hot  gases  thus 
produced  to  actuate  a  mechanism  by  the  action  of  expanding 
gas  on  a  moving  part. 

I.  The  air  and  fuel  supply  may  be  accomplished  in  any  of  the 
ways  known  to  and  accepted  by  engineers  ;  the  results  cannot  vary 
much  with  changes  in  design  of  this  part,  since  compressors  and 
pumps  are  well-known  machines. 

II.  The  burning  of  the  fuel  in  the  air  supplied  offers  what  is 
probably  the  most  difficult  problem  for  solution.     Its  difficulty 
is  attested  by  the  variety  of  the  means  proposed  and  the  indif- 
ferent success  of  those  that  have  been  tried.     When  solid  fuel 
was  used,  as  in  Cayley's  engine,  no  means,  without  great  compli- 
cation of  parts,  were  found  adequate  to  cope  with  the  smoke,  dust, 
and  distillation  of  gas  from  the  coal.     With  liquid  fuel,  Bray- 
ton   was  troubled  with  soot,   and   those   burners  which   have 
burned  clean  required  a  large  excess  of  air.    With  gas,  Brayton 
also  failed,  and  he  was  not  alone,  as  no  adequate  system  of  burn- 
ing gas,  when  enclosed  and  under  pressure,  had  then  been  pro- 
posed, the  trouble  being  not  so  much  in  getting  a  burner  to  work 
under  specified  conditions,  as  to  get  one  that  would  work  under 
wide  and  sudden  variations  of  feed  and  pressure. 

III.  The  utilization  of  the  hot  gases  has  been  successfully 
tried  in  cylinders,  and  rotary  machines  have  been  proposed,  in- 
cluding the  turbine ;  though  none  have  appeared  on  the  market, 
ifc  is  inconceivable  that  there   can  be   any  serious   trouble   to 
be  anticipated  in  such  utilization.     The  reason  of  the  general 
failure    of   the   machines   proposed  is   probably   the   difficulty 
noted  above,  for  gases  at  high  temperature  are  used  every  day 
in  exploding  engines  with  the  greatest  ease.     All  of  these  non- 
explosive  engines  may  work  under  any  one  of  several  cycles, 
depending   on  the  relation  between  the  last  two  processes— 
the  amount  of  heating  compared  with  the  amount  of  expansion 
permitted.     Here  is  an  important  point,  for  by  a  simple  control 
of  the  above  relations,  by  passing  air  around  the  fire  and  vary- 
ing the  cut-off  to  the  power  cylinder,  we   can  vary  the  cycle, 
hence  the  work  output ;  thus  an  engine  equipped  with  means  to 
do  this  would  be  able  to  work  at  all  loads  equally  well,  and  be 
able  to  pull  up  to  a  temporary  overload,  just  as  do  steam  engines. 
This  great  elasticity  of  action  is   beyond  comparison  with  the 


20  THE   HEAT-ENGINE  PROBLEM. 

rigidity  of  the  explosive  engine.  Moreover,  the  question  of 
available  fuel  again  comes  up  ;  anything  that  will  burn  may  be 
used,  and  with  it  a  working  elasticity  obtained  -  two  desirable 
results. 

Before  we  examine  the  details  entering  into  engine  construc- 
tion, let  us  look  at  some  of  the  complete  machines  that  have 
been  proposed  for  carrying  out  the  system,  dividing  our  study 
according  to  the  fuel  used,  taking  up,  first,  coal-burning  ;  second, 
oil-burning;  and  third,  gas-burning  engines. 

Coal-bu  r  n  ing  En  gin  es . 

18.  The  first  working  engine  of  this  class  was  Cay  ley's  furnace- 
gas  engine.     The  air  was  forced  into  the  fire-box,  where  a  coal 
fire  was  maintained,  and  the  hot  gases  used  in  a  cylinder.     This 
engine   worked  on  what  has  been  called  the    Brayton    cycle. 
Rankine  says  of  it :  "  The  cylinder,  piston,  and  valves  were  found 
to  be  so  rapidly  destroyed  by  the  intense  heat  and  dust  from  the 
fuel  that  no  attempt  was  made  to  bring  it  into  use." 

In  the  United  States,  Philander  Shaw  proposed  the  engine  of 
Figs.  17  and  18  in  1861.  Air  from  a  pump  cylinder  passes  more 
or  less  through  a  coal  fire,  becoming  heated  in  its  conversion,  and 
finally  with  increased  volume  working  in  a  larger  power  cylin- 
der. The  fire-box  is  provided  with  a  grate,  c,  and  is  lined  with 
brick  e/(Fig.  17),  fuel  is  fed  through  //(Fig.  18),  and  is  moved 
by  a  piston  head  g.  The  furnace  has  openings,  a\  below  the  grate, 
and  others,  a2,  above  the  fuel.  Two  single-acting  cylinders  are  con- 
nected at  180  degrees  to  one  shaft.  Each  cylinder  is  in  two  parts  : 
the  upper,  A,  is  finished  to  a  fit  with  piston  D  •  the  lower  part, 
J5,  is  left  rough,  as  the  lower  part,  F,  of  the  piston  does  not  touch 
it.  The  top  of  the  piston  has  a  trunk,  C,  which  acts  as  an  air- 
pump  cylinder  with  the  main  cylinder  casing.  The  motion  of  the 
air  is  indicated  by  the  arrows,  and  the  proportion  that  enters  the 
fire-box  above  or  below  the  fuel  is  controlled  by  a  valve  r  (Fig. 
17).  The  heated  air  and  gaseous  products  of  combustion  pass 
into  the  cylinder  through  valve  p,  and  the  exhaust  passes  out 
through  a  heater  for  incoming  compressed  air.  A  little  flange, 
#,  is  placed  to  catch  dust  and  a  groove,  v,  for  oil. 

19.  All  parts  where  radiation  is  likely  to  occur  are  jacketed 
by  the  incoming  air.    The  working  part  of  the  piston  fits  loosely, 
and  at  a  point  just  above  the  highest  position  of  its  bottom  is  an 


THE    HEAT-ENGINE   PROBLEM. 


22 


THE   HEAT-ENGINE  PROBLEM. 


annular  space  kept  filled  with  cool  air  to  prevent  overheating  of 
the  working  faces.  Governing  may  be  made  two-fold  :  first,  the 
amount  of  heat  added  fco  the  air  can  be  regulated  by  sending 
more  or  less  through  the  fire  ;  and,  second,  the  power  may  be 
directly  controlled  by  the  main  cylinder  cut-off.  The  air  receives 
heat  really  from  one  source,  though  in  two  places — the  one  source 
being  the  fire,  and  the  two  places  the  exhaust-warmed  pre- 
heater,  or  regenerator,  and  the  fire-box.  A  hand  pump  is  pro- 
posed to  raise  the  internal  pressure  for  starting. 

20.  The  engine  proposed  by  Henry  Messer  in  1863  is  shown 
in  Figs.  19-21.      The  air  pump  is  double-acting,  and  the  power 


FIG.  19. 


JLJL 


FIG.  80. 


THE   HEAT-ENGINE   PROBLEM. 


23 


cylinder  single-acting,  hence  there  are  two  stages  :  1.  On  the 
down-stroke  air  is  compressed  and  heated  at  decreasing 
volume ;  2.  On  the  up  stroke  the  air,  previously  compressed 
and  heated,  is  sent  through  the  fire  and  thence  to  the  working 
cylinder.  When  the  up-stroke  begins,  the  high-pressure  gases 
in  the  reservoir  begin  to  expand  at  the  same  time  that  the  air 
in  the  pump  begins  to  increase  in  pressure,  and,  finally,  when 
the  increasing  pressure  in  the  pump  equals  the  decreasing  pres- 
sure in  the  receiver  the  second  cylinderful  of  air  becomes  avail- 
able. In  its  passage  the  air  may  take  up  enough  heat  to  maintain 
p  constant,  T  constant,  or  neither  ;  it  is  impossible  to  say,  hence 


FIG.  22. 

the  cycle  is  indeterminate.  Later  Messer  suggests  some  changes 
in  valve  construction  to  prevent  overheating,  also  in  governing 
by  throttling  between  the  fire  and  air  receiver. 

21.  Cyrus  W.  Baldwin  proposed  the  engine  of  Fig.  22  in  1865. 
The  engine  cylinder  has  between  its  upper  cool  part  and  lower 
hot  part  an  //-shaped  water  passage  f  in  accordance  with  his 
belief  that  more  trouble  with  overheated  working  faces  will  be 
caused  by  heat  conducted  through  the  metal  cylinder  walls  than 
by  contact  with  the  hot  gases.  He  provides  for  distilling  gases 
from  the  coal  fire  by  supplying  an  auxiliary  fire  beyond  the  main 
furnace.  He  says  :  "  Part  of  the  fuel  in  the  large  furnace  is 
changed  by  the  heat  therein  to  volatile  gases,  which  do  not  burn 
when  generated,  but  will  burn  if,  while  they  are  hot,  they  are 


24  THE   HEAT-ENGINE  PROBLEM. 

brought  into  flame.  To  supply  such  a  flame  through  which  all 
the  products  of  combustion  from  the  large  furnace  must  pass, 
a  small  furnace  is  supplied,  and  the  results  which  follow  its 
application  are  found  in  practice  to  be  highly  beneficial." 

22.  In  the    engine  of  L    A.  L.  Soclerstrom,  1869,    a  radical 
change  of  arrangement  is  proposed,  as  shown  in  Fig.  23.     The 


FIG.  23. 

upper  part  of  the  cylinder  acts  as  the  compressor  and  sends  air 
down  and  around  the  casing,  the  air  passing  the  exhaust  reheat- 
ing coil  B.  After  this  reheating  by  contact  with  the  exhaust 
coil  the  air  is  sent  out  through  the  opening  yx  on  top  of  the  fire 
at  a,  the  top  combustion  helping  to  prevent  coking  and  distilla- 
tion, but  adding  trouble  from  dust  and  ash.  Governing  is  effected 
by  a  split  current  and  variable  cut-off. 


THE   HEAT-ENGINE   PROBLEM. 


25 


23.  Thomas  M.  Fell  in  1880  proposed  a  very  interesting 
though  complicated  machine  (Fig.  24).  An  air  compressor,  C\ 
sends  air  through  the  pipe  Ml  to  the  fire  at  A.  Exhaust  gases 
from  the  power  cylinder  A1  are  thrown  first  around  the  tubes 
D\  and  then  around  the  water- cooled  tubes  El,  and  are  returned 
by  the  pump  J3l,  through  the  tubes  D\  and  back  to  the  hot 
chamber  T  through  the  valve  IP.  Accumulation  of  gases  in 
the  closed  system  is  prevented  by  the  blow-off  Gl,  arranged  to 
maintain  a  constant  pressure  on  the  high-pressure  side  of  the 
system.  An  attempt  is  made  to  keep  a  two-par  1;  system,  one 


FJG.  24. 

high-pressure  heating,  and  the  other  low-pressure  cooling.  This 
system  would  probably  give  the  results  of  Cycle  IIIC.,  OL'  one 
somewhat  similar. 

24.  Hiram  S.  Maxim  in  18S4  proposed  a  machine  as  shown  in 
Fig.  25.  Air  is  drawn  by  the  right-hand  side  of  the  piston  from 
the  space  A',  which  in  turn  gets  its  supply  from  the  atmosphere 
by  a  throttling  slide  T.  This  space  A1  has  a  diaphragm  E  so 
arranged  that  a  partial  vacuum  will  cause  the  slide  valve  N  to 
by-pass  air  around  the  fire.  In  its  normal  operation,  or  when 
running  slowly,  most  of  the  air  passes  through  the  fire  and  is 
heated.  At  the  time  the  air  is  passing  into  the  receiving  cham- 
ber no  air  is  entering  the  working  side  of  the  cylinder.  Hence 


26 


THE   HEAT-ENGINE   PROBLEM. 


the  heating  of  the  air  during  this  stage  must  take  place  at  de- 
creasing volume  and  increasing  pressure.  When  this  is  finished, 
the  valve  V  opens  and  gases  enter  on  the  impelling  side  of  the 
piston.  The  tendency  now  is  to  decrease  pressure,  but  air  in 
the  space  G l  will  pass  the  fire,  tending  to  uphold  pressure  ;  hence 
there  is  a  second  heating  at  uncertain  pressure,  giving  an  inde- 
terminate cycle. 

25.  Lucien  Genty  in  1893  proposed  the  engine  of  Figs.  26-28. 
This  engine  has  the  usual  single-acting  cylinder  with  elongated 


piston.  Air  is  drawn  from  a  chamber  under  the  floor  to  obviate 
the  noise  of  suction.  The  air  thus  received  by  the  water-jacketed 
compressor  10  is  sent  through  the  valves  17  into  the  hollow 
bed  4,  and  thence  past  the  ribbed-coil  preheater,  here  to  be 
warmed  by  the  exhaust.  The  preheater  is  arranged  to  take  up 
expansion,  and  exhaust  gases  are  prevented  from  touching  the 
metal  by  brick  lining.  The  partly  heated  air  enters  admission 
valve  36  by  pipe  35.  Yalve  36  is  double  balanced,  and  held  to 
its  seat  by  a  helical  spring,  and  is  actuated  by  a  cam  on  the 
horizontal  shaft. 


THE   HEAT-ENGINE   PROBLEM. 


27 


2G.  The  valve  gear  is  arranged  to  govern  by  varying  the  open- 
ing of  valve  36.  A  weighted  piston  controller  regulates  the  pro- 
portion of  air  admitted  to  the  two  passages  41  and  42  after  pass- 
ing the  admission  valve  36.  Thus  the  method  of  governing  is 
two-fold  ;  1,  by  a  variable  cut-off  to  the  power  cylinder  and  com- 
bustion chamber,  and  2,  by  means  of  keeping  the  pressure  of 
the  air  admitted  initially  constant.  Passage  42  leads  above  the 
fire  and  41  below. 


FIG.  26. 


The  combustion  chamber  is  a  cast-iron  funnel  lined  with 
brick,  enlarged  at  the  bottom  ;  the  coal  is  thus  burned  without  a 
grate.  The  lower  and  hottest  part  has  a  water-jacket,  49.  Means 
for  charging  and  cleaning  are  provided,  and  a  ball-and-socket 
swivel,  57,  carries  a  stirrer,  58,  which  is  removable.  After  pass- 
ing the  admission  valve  and  reaching  the  fire,  the  air  is  first 
heated  and  afterwards  expanded  in  the  presence  of  the  fire  under 
the  piston.  The  motor  cylinder  is  of  two  parts  ;  the  lower,  72,  is 
lined  with  fire  clay,  the  upper,  74,  is  bored  true  and  water-jack- 
eted. The  lower  part  of  the  piston  has  air-cooling  ribs,  76,  and 
the  rod  is  rigidly  connected  to  the  yoke  78,  leaving  no  lubri- 
cated joint  within  the  piston.  The  piston  fits  loosely  in  parts 


28 


THE   HEAT-ENGINE   PROBLEM. 


75  and  78,  and  tight  in  part  74.  Besides  having  the  water- 
jacket  on  this  part  it  may  be  further  protected  from  heat  and 
dust  by  a  groove,  feeding  air  down  to  the  combustion  chamber ; 
to  do  this  air  is  provided  by  a  small  pump  on  the  piston  at  89. 
A  flexible  pipe  provides  water  to  cool  the  piston  interior. 

27.  After  being  heated  and  expanded  the  gases  are  discharged 
through  the  self- cleaning  valve,  110.  This  valve  is  hollow  and 
water-cooled,  as  is  also  its  casing,  116.  Compressed  air  seats 
the  valve,  and  mechanism  raises  it.  Injury  from  sparks,  etc.,  is 


FIG.  28. 


prevented  by  drawing  the  valve  up  in  its  sleeve  casing.  To  pro- 
tect the  seat  it  is  made  narrow  and  cleaned  by  escaping  air. 
Exhaust  gases  are  discharged  through  the  regenerator,  or  pre- 
heater.  This  machine,  though  very  complicated,  presents  many 
suggestions  that  may  be  of  value. 

It  will  be  observed  that  the  combustion  of  coal  calls  for  a 
great  complexity  of  parts  and  functions,  and  this  must  be  so. 
We  have,  as  one  of  the  greatest  troubles,  the  impossibility  of 
regulating  the  heating  power  with  time  of  a  coal  fire,  and  there 
is  the  inevitable  dust  and  ash.  This  makes  the  use  of  oil  and 


THE   HEAT-ENGINE   PROBLEM. 


29 


gas  with  the  necessarily  simplified  apparatus  almost  mandatory 
in  internal-combustion  engines,  especially  those  of  moderate  size. 
While  here  we  should  have  none  of  the  coal  troubles,  we  will 
meet  others  incidental  to  the  feeding  of  fuel  as  it  is  required, 
and  only  for  the  instant  that  it  is  required. 

Oil-burning  Engines. 

28.  In  1865  Stephen  Wilcox,   Jr.,    proposed    an   oil  burning 
engine,  shown  in  Fig.  29.     He  said,  "  The  extraordinary  devel- 


FIG.  29. 

poment  of  what  is  known  as  petroleum  oil  and  the  several  prod- 
ucts obtained  therefrom,  makes  it  practicable  to  produce  and 
work  very  small  engines  on  this  plan." 

A,  the  working  cylinder,  and  a1,  the  pump,  differ  in  no  part 
from  what  we  have  seen  in  the  coal-burning  engines.  The 
means  for  feeding  and  burning  the  oil  are,  however,  new  and  of 
especial  interest.  Fuel  is  fed  from  an  elevated  tank  1  through 
pipe  2 ;  the  interior  pressure  of  the  furnace  is  balanced  on  the 
surface  of  the  oil  by  pipe  3.  A  stop-cock,  4,  is  provided,  which 
is  arranged  to  shut  off  oil  by  a  piston  and  links,  when  the 
furnace  pressure  exceeds  what  is  desired ;  this  serves  to  govern 


30 


THE   HEAT-ENGINE   PROBLEM. 


the  machine.  Oil  flows  into  a  vaporizing  reservoir,  12  (Fig. 
33),  having  Ings,  13,  to  conduct  heat  from  above.  The  upper 
part  of  this  reservoir  is  cylindrical  and  provided  with  holes, 
10,  and  fitted  with  a  loose  part,  11,  with  inclined  top  and  a  hole 
in  the  centre  matching  the  movable  pin,  14,  actuated  by  the 
governor.  This  pin  and  hole  act  to  close  the  vapor  outlet.  The 
special  construction  of  the  burner  is  intended  to  give  a  constant 
velocity  of  efflux  to  the  vapor. 

This  combustion  may  be  classed  as  the  burning  of  a  jefc  of 
vapor  in  an  atmosphere  of  air,  the  air  about  the  flame  being 
kept  fresh  only  by  convection. 

Governing  is  effected  by  a  double  means  ;  the  fly-balls  act  to 
shut  off  vapor  and  increase  of  pressure  cuts  off  the  fuel. 


29.  A.  H.  De  Villeneure  in  1872  proposed  an  engine  in  which 
lie  provided  a  combustion  chamber,  having  a  platinum  rose,  p 
(Fig.  30),  on  which  impinge  jets  of  oil  vapor  from  b  and  air  from 
m  provided  by  pumps.  He  thus  expects  to  obtain  a  combustion 
to  heat  the  mixture. 

George  B.  Brayton  in  1872  proposed  and  built  an  engine  that 
was  very  complete  and  fairly  successful.  Fig.  31  is  a  general 
view  and  Fig.  32  his  oil  burner. 

Air  is  compressed  in  the  single-acting  pump,  which  has  a  vol- 
ume one-half  that  of  the  power  cylinder.  The  compressed  air 
passes  from  the  constant-pressure  receiver  through  pipe  1)  and 
over  the  absorbent  material  e,  through  which  the  fuel  is  fed  by 
a  pump.  Here  it  takes  up  vapor  and  the  mixture  passes  the 
wire-gauge  grating  and  into  the  cylinder,  where  it  burns. 


THE   HEAT-ENGINE  PROBLEM. 


31 


Means  are  provided  to  prevent  entirely  shutting  off  the  air  from 
the  power  cylinder,  and  thus  there  is  kept  constantly  burning  a 
small  flame  which  increases  for  the  power  stroke.  Governing 
is  effected  by  a  variable  cut-off  to  the  power  cylinder. 

The  power  cylinder  is  water-jacketed,  and  no  trouble  is  ex- 
perienced through  overheating.  A  safety  valve  is  placed  on 
the  reservoir. 


32 


THE   HEAT-ENGINE   PROBLEM. 


30.  Joseph  Hirsch,  in  1874,  proposed  the  engine  shown  in 
Fig.  33.  An  air  pump,  L,  supplies  air  to  a  cylinder,  //,  to  take 
the  place  of  converted  air  which  is  periodically  expelled ;  J  is  a 
regenerator  connecting  the  two  cylinders,  A  and  ///  N  is  a 
water  chamber  for  cooling  gases.  Fuel  is  injected  at  I>'2.  When 
the  piston  C  moves  down,  air  from  G  is  sent  over  through  the 
regenerator,  partly  heated  here  and  then  further  heated  by 
fuel  at  B\  On  the  up-stroke  the  products  of  combustion  pass 
over  the  regenerator  to  //,  being  thus  doubly  cooled,  first  by 
the  regenerator  and  second  by  the  injected  water.  Part  of  the 
products  of  combustion  escape  at  k  and  are  replaced  by  fresh 
air.  No  means  for  ensuring  the  combustion  of  fuel  in  the 
atmosphere  of  air  and  products  of  combustion  are  provided. 


FIG.  33. 

31.  Stephen  Wilcox,  in  1885,  proposed  the  engine  of  Figs.  34 
and  35.  The  power  cylinder,  A,  is  double-acting  and  tande re- 
connected to  an  air  compressor,  B.  Plates  of  non-conducting 
material  are  applied  to  piston  and  cylinder  heads  to  keep  the 
gases  admitted  as  hot  as  possible.  Cylinder  walls,  where  lubri- 
cation is  necessary,  are  water-jacketed,  and  water-cooled  rocking 
valves  of  the  Corliss  type  are  provided  ;  air  is  sent  to  the  exhaust 
preheater  C  from  the  pump  before  passing  to  the  power  cylinder, 
and  is,  therefore,  first  warmed  and  later  heated  by  combustion, 
in  its  passage  over  the  gauze  grating,  8,  where  it  meets  the 
liquid  fuel.  The  valve  mechanism  permits  varying  the  cut-off 
and  reversing. 

A  reciprocating  tube  carrying  a  lamp  works  in  each  port  r 
and  serves  as  an  igniter  in  connection  with  an  exterior  relighter. 


THE    HEAT-ENGINE   PROBLEM. 


33 


The  receiver  is  first  charged  with  air  by  a  hand-pump,  and  a 
little  fuel  sent  to  the  burner  by  hand.  Valve  24  in  the  escape 
pipe  22  is  closed  and  a  torch  applied  to  the  burner  through  w-. 
The  engine  may  now  be  started  by  opening  the  main  stop-valve, 
28,  and  automatic  action  begins. 

32.  Kudolph  Diesel,  in  1892,  proposed  the  oil-burning  motor 
shown  in  Fig.  36.  A  single-acting  cylinder  C carries  the  plunger 


FIG.  34.  |  T 

P,  air-valve  F,  and  fuel-valve  D.  High  compression  of  the  air 
is  followed  by  fuel  injection  and  later  by  expansion.  The  tem- 
perature developed  by  the  compression  must  be  sufficient  to 
ignite  any  fuel  thrown  into  the  air.  Later  engines  vary  some- 
what in  detail,  but  the  principle  of  operation  is  the  same. 
Gaseous  and  powdered  solid  fuel  can  also  be  used. 

It  is  obvious  that  the  quantity  of  fuel  injected  per  stroke  will 
determine  the  cycle.     If  only  sufficient  isjfadmitted  to  keep  T 
3 


34  THE   HEAT-ENGINE   PEOBLEM. 

constant,  we  have  Cycle  IV.,  or  some  of  its  variations ;  if  enough 
heat  'results  to  keep  p  constant  during  combustion,  we  have 
one  of  the  Cycles  III. 

33.  B.  V.  Nordberg  and  C.  E.  Shadall  proposed  in  1895,  not 
a  complete  engine,  but  a  system  of  operating  engines  by  internal 
combustion  ;  the  apparatus  is  shown  in  Fig.  37.  The  products 
of  combustion  are  to  be  used  in  any  way  deemed  advisable. 


FIG.  35. 


A  source  of  airjsupply  and  means  for  using  the  products  are 
assumed.  Oil  is  fed  from  a  tank  B  by  water  displacement,  the 
same  water-jacketing  the  combustion  chamber  C.  This  com- 
bustion-chamber jacket  may  add  steam  to  the  products  at  c^ 
The  air  current  from  the  compressor  acts  (1)  on  the  surface  of 
the  water  A  ;  (2)  at  the  oil  atomizer  E;  (3)  at  the  lamp  /;  and 
(4)  with  reduced  pressure  atjhe_opening  c  in  the  burner.  The 


THE    HEAT-ENGINE    PROBLEM. 


35 


atomizer  is  fed  with  oil  through  the  pipe  b,  and  the  float 7>,3  pre- 
vents, by  proper  specific  gravity,  an  overflow  of  water.  The  oil 
passes  up  to  the  nozzle,  where  it  meets  an  air  current  and  is 
there  sprayed  into  the  chamber  C1 ;  the  spray  meeting  a  flame 
jet  from  the  lamp  at  i  in  an  atmosphere  of  air  provided  through 
c,  is  enabled  to  burn.  Increased  pressure  cuts  off  the  oil  supply 


Oil 


FIG.  36. 

Gas-burning  Engines. 

31  The  operation  of  engines  of  the  class  we>re  considering 
by  a  gas  combustion  offers  what  would  seem  tcvbe  the  simplest 
solution,  but  in  reality  the  difficulty  is  much  greater  than  might 
be  supposed.  Of  course,  no  trouble  will  be  ^experienced  with 
dust,  vaporizing  of  oil,  or  soot  from  imperfect  oil  combustion, 
but  there  appears  the  difficulty  of  finding  a  burner  which  will 


36 


THE   HEAT-ENGINE   PROBLEM. 


THE   HEAT-ENGINE   PROBLEM. 


37 


completely  consume  the  gas  without  excess  of  oxygen  under  the 
widest  possible  range  of  conditions.  The  engines  proposed 
differ  chiefly  in  the  means  proposed  for  accomplishing  this  gas 
combustion. 

Stephen  Wilcox,  in  1865,  proposed  the  machine  of  Fig.  38. 
Air  and  gas  are  supplied  through  pipes  K  and  J  from  feed- 
pumps G  and  If  to  burner  j,  and  the  mixture  is  ignitejd  at  R. 
When  the  gas  is  to  be  supplied  by  vaporizing  oil,  the  exhaust- 
heated  vaporizer  N  is  introduced.  A  is  the  power  cylinder,  B 
a  changing  cylinder,  and  F  a  regenerator.  When  b  descends,  the 
valve  M  allows  cold  air  to  fill  the  top  of  B  ;  this  air,  on  the  up- 


Fio.  38. 

stroke,  moves  through  the  regenerator  and  burner,  which  at 
this  time  delivers  its  mixture  ;  this  double  heating  raises  the 
pressure  in  the  system,  and  the  piston  rises.  Then  both  de- 
scend and  exhaust  some  gases  into  P.  The  engine  is  thus  oper-  ' 
ated  not  solely  through  the  heating  of  products  of  combustion, 
but  by  the  heating  of  a  mixture  of  these  gases  with  pure  air. 

35.  Albert  Schmid  and  J.  C.  Beckfeld  proposed,  in  1889,  the 
system  of  obtaining  hot  gases  through  internal  combustion  of 
air  and  gas  by  the  apparatus  of  Fig.  39.  Gas  and  air  are  sup- 
plied by  pumps  to  tanks  A  and  G ;  they  are  mingled  in  an 
injector  chamber  $2 ;  thence  passing  through  the  perforations  t, 
they  are  burned  at  8.  To  maintain  a  difference  of  pressure  in 


38 


THE   HEAT-ENGINE   PROBLEM. 


the  tanks  and  combustion  chamber  a  relief  valve  0,  controlled 
by  a  diaphragm,  is  provided.  To  dilute  the  products  of  com- 
bustion and  reduce  their  temperature,  a  pipe  L  conducts  fresh 
air  to  the  mixer  Sl.  Electric  ignition  is  suggested. 

Later,  another  arrangement,  shown  in  Fig.  40,  was  suggested. 
Here  a  long  perforated  brick  0  is  inserted  to  aid  combustion 
and  act^s  a  reigniter.  A  receiving  reservoir  is  added,  to  which 
the  blow-off  is  attached.  An  igniting  plug  V  of  coke  or  carbon 
is  also  added. 

In  Fig.  41  is  shown  an  addition  of  a  steam  boiler  with  an  ex- 


FlG 


haust  gas  feed^water  heater.  The  boiler  is  to  be  used  in  start- 
ing with  an  ordinary  external  combustion  fire-box,  and,  later, 
enclosed,  mixing  the  steam  and  products  of  combustion. 

36.  Ilerman  Schumm,  in  1895,  suggested  the  engine  of  Figs. 
42  and  43,  which  offers  some  novelty.  A  is  the  engine  cylinder, 
B  the  piston,  C  an  inlet  for  combustible  mixture,  D  an  inlet  for 
pure  air,  and  E  the*,  exhaust  valve.  An  electric  igniter,  i,  is 
provided,  and  a  gauze  diaphragm,  g,  prevents  back  flash.  Air 
is  compressed  by  the  pump  and  stored  in  6r,  gas  similarly  com- 
pressed by  H.  Air  is  admitted  through  J)  until  the  piston  has 
moved  out  a  short  distance  and  then  cut  off;  at  the  same  time 


THE   HEAT-ENGINE   PROBLEM. 


39 


the  air  and  gas  mixture  is  admitted  through  C  and  ignited,  the 
combustion  operating  on  the  gauze  until  the  mixture  F^is  in  turn 
shut  off,  when  adiabatic  expansion  begins. 

37.  Sydney  A.  Eeeve,  in  1897,  proposed  the  apparatus  of  Fig. 


FIG.  40. 


44  to  obtain  by  internal  combustion  working  gases  to  be 
used  in  an  engine.  He  lays  stress  on  two  points :  one,  re- 
lating to  the  combustion,  that  the  proportions  of  fuel  to  air 
shall  not  materially  vary ;  and  the  other,  the  reduction  of  the 


FIG.  41. 


temperature  before  sending  the  products  of  combustion  to  the 
engine. 

Both  air  and   fuel   are  to  be   supplied  by  separate  pumps, 
and  the  proportions  regulated  by  maintaining  the  pressures  in 


40 


THE   HEAT-ENGINE   PROBLEM. 


the  two  receivers,  C  and  Cl,  equal  by  water  seal  and  float  valve, 
and  by  passing  these  gases  of  equal  pressure  through  a  double- 
ported  valve  D  of  proper  areas.  The  pressure  in  C  is  controlled 
by  that  in  C1,  and  that  in  C  kept  above  that  in  the  combustion 
chamber  by  the  loaded  check  G.  This  also  permits  mixing 
fresh  air  with  the  "products  of  combustion  if  more  than  is 
wanted  for  combustion  is  available. 

The  products  of  combustion  pass  through  water  so  supplied  as 
to  keep  a  given  quantity  always  on  hand  and  at  the  boiling  point 


FIG.  42. 

corresponding  to  the  pressure,  so  that  the  hot  gases  will,  in  part- 
ing with  their  heat,  evaporate  water  and  be  themselves  cooled  to 
the  temperature  of  saturated  steam  at  their  pressure.  Of  course, 
any  feed-water  supplied  must  be  heated  before  evaporation,  but 
this  only  has  the  effect  of  decreasing  the  rate  of  evaporation 
without  stopping  it. 

Another  device  proposed  for  equalizing  pressures  in  the  air 
and  gas  receivers  is  to  let  fuel  pass  through  a  flexible-walled 
bag  suspended  in  the  air  tank. 

38.  The  cooler  and  burner  might  also  be  arranged  as  shown 


THE   HEAT-ENGINE   PROBLEM. 

in  Fig.  45.  The  regulator  valve  has  a  spring-balanced  dia- 
phragm, 4,  which  actuates  a  similar  plunger,  6,  by  rod  5,  the 
plunger  moving  in  a  perforated  sleeve.  Gas  enters  through  tube 
12  in  the  centre  and  air  through  10,  the  mixture  passing  an 
igniter  at  b.  A  liquid  seal  is  provided  here  for  maintaining  a 
decrease  of  pressure  between  supply  and  discharge  valves. 

39.  Lucius  T.  Gibbs,  in  1897,  proposed  a  system  (Fig.  46),  in 
which  the  motive  power  shall  be  air  admitted  to  the  power 
cylinder  from  a  source  under  pressure,  and  when  the  pressure 
after  cut-off  has  become  so  far  reduced  as  to  reach  that  of  a 


FIG.  44. 

stored  mass  of  gas  maintained  lower  than  the  air  supply,  the 
gas  will  enter  and  be  ignited,  thus  tending  to  keep  up  the  pres. 
sure  during  the  expansion.  Thus  the  adiabatic  will  be  raised 
to  perhaps  an  isothermal  or  higher. 

40.  If  we  would  trace  any  line  of  progress  through  these 
machines,  we  could  not  make  our  division  according  to  the  fuel 
used,  as  at  times  engines  burning  all  kinds  of  fuels  have  been 
suggested  simultaneously.  To  be  sure,  before  the  possibilities 
of  petroleum  were  known,  the  principal  fuel  was  coal,  and, 
naturally,  in  early  engines  coal  fires  predominate ;  though  it 
would  seem  that  they  would  gladly  be  dropped  for  oil  and  gas, 
yet  they  were  not,  and  continue  to  appear  from  time  to  time 


42 


THE   HEAT-ENGINE   PROBLEM. 


There  is  a  division,  however,  in  the  stages  of  progress  that  is 
significant,  as  showing  how  strong  is  the  influence  of  the  known 
and  tried  on  the  proposals  of  apparent  novelty.  The  old  so- 
called  hot-air  engines  of  the  Ericsson  type  had  a' mass  of  air 


FIG.  45. 

enclosed,  and  means  were  provided  for  heating  and  cooling  the 
same  mass  without  exhausting,  the  heat,  of  course,  being  sup- 
plied through  walls  from  an  outside  fire.  So  we  find  the  earlier 
internal-combustion  engines  working  on  a  system  only  slightly 
different  from  the  above.  There  is  a  mass  of  gases  enclosed, 


THE   HEAT-ENGINE   PROBLEM.  43 

and  means  for  transferring  them  from  a  hot  part  to  a  cold  part, 
and  so  varying  their  internal  pressure,  but  the  hot  part  is  here 
provided  for  not  by  a  hot  plate,  but  by  a  short  flame  injection, 
or  passage  over  a  fire.  The  operation  was  to  depend  chiefly  on 
the  alternation  of  hot  and  cold  in  the  same  mass. 

41.  Later  this  system  was  developed  by  injecting  more  and 
more  fuel,  or  by  causing  the  mass  to  pass  entirely  through  the 
fire,  necessitating  more  fresh  air  for  the  next  time  and  calling 
for  an  exhaust ;  finally  we  have  a  regular  admission  and  exhaust, 
the  gases  passing  continuously  in  the  same  direction,  and  no 
alternation  of  heating  and  cooling  being  attempted  in  the  sys- 
tem. Any  cooling  that  is  to  to  take  place  must  occur  'outside 


FIG.  46. 


the  machine  in  the  atmosphere,  and  the  resulting  contraction 
of  the  gases  forms  no  part  of  the  working  cycle. 

42.  The  engines  presented  represent  by  no  means  all  of  those 
suggested,  but  are  selected  from  a  very  large  number  to  show 
the  principal  ideas  advanced  in  the  past.  By  studying  them  we 
can  reach  an  understanding  of  what  points  may  be  accepted  as 
solved,  and  what  are  still  open  for  discussion  and  research. 

It  will  be  observed  that  these  non-explosive  internal-combus- 
tion engines  may  be  divided  into  (I.)  intermittent  internal  com- 
bustion, as  in  Genty's,  Brayton's,  Wilcox's,  Diesel's,  etc.,  in 
which  the  air  and  fuel  pass  the  power- cylinder  valves  before 
combustion ;  and  (II.)  continuous  internal  combustion,  as  sug- 
gested by  Schmid  and  Beckfeld,  Reeve,  and  Nordberg  and 
Shadall,  in  which  the  hot  gases  are  continuously  produced,  and 
afterward  utilized  by  passing  through  valves  to  the  power 
cylinder,  or  by  expanding  through  a  turbine  without  valves. 


44  THE   HEAT-ENGINE   PROBLEM. 

43.  Different  ways  of  doing  the  same  thing  by  varying  details 
have  been  advanced,  and  it  may  be  well  to  bring  these  together 
in  some  cases  for  comparison. 

Cylinders  : 

Both  single  and  double  acting,  jacketed  and  unjacketed  are 
found.  Air  and  power  cylinders  may  be  independent,  or  the 
two  operations  of  compression  and  expansion  performed  in 
opposite  ends  of  the  same  cylinder.  When  this  is  done,  the 
cylinder  may  be  of  the  same  diameter  throughout,  or  reduced 
at  one  end.  Independent  cylinders  have  been  connected  by 
beam,  separate  cranks  on  the  same  shaft,  and  in  tandem.  In 
most  of  the  intermittent-combustion  type  the  piston  fits  a  part 
of  the  cylinder  only,  and  is  loose  in  the  hot  end  ;  in  this  case, 
heat  is  prevented  from  reaching  the  working  faces  by  prolong- 
ing the  piston,  and  by  blowing  cold  air  or  steam  down  around 
the  loose  part  toward  the  hot  end. 

44.  Igniters : 

With  engines  using  oil  or  gas,  where  combustion  may  be 
entirely  interrupted  for  a  time,  some  form  of  relighter  must  be 
provided.  This  may  be 

I.  A  plate  heated  by  an  external  jet  from  outside.    Nordberg. 

II.  A  platinum  rose,  with  mixture  impinging.     Yilleneure. 

III.  High  temperature  of  compression.     Diesel. 

IV.  A  plate  or  wire  electrically  heated.     Wilcox. 

Y.  Introduction  of  incandescent  solid.    Schmid  and  Beckfeld. 

VI.  Electrodes  with  spark  gap.     Babcock. 

VII.  Introduction  of  auxiliary  flame  continuously.    Nordberg 
and  Shadall. 

VIII.  Introduction  of  auxiliary  flame  intermittently.    Wilcox. 

IX.  Constant-burning  flame  in  cylinder.     Brayton. 

45.  Use  of  water  : 

I.  In  compression  to  cool  air. 

II.  To  be  evaporated  by  products  of  combustion  by  contact 
and  adding  steam  produced. 

III.  To  cool  expanded  gases  and  produce  pa.rtial  vacuum. 

IV.  To  cool  hot  parts  and  be  discharged. 

V.  To  cool  hot  parts  and  add  steam. 

VI.  In  an  internally  fired  steam  boiler,  which  may  act  as  a 
starter. 

VII.  As  a  jacket  to  hot  parts,  the  steam  used  in  a  separate 
cylinder. 


THE    HEAT-ENGINE    PROBLEM.  45 

VIII.  As  an  annular  piston  cooler  to  prevent  contact  of  hot 
gases  with  working  face  of  cylinder. 

46.  Methods  of  governing  ; 

I.  Throttling  air  intake. 

II.  Throttling  passage  between  the  air  and  power  cylinders. 

III.  Varying  cut-off  at  power  cylinder  inlet. 

IV.  Varying  combustion  chamber  pressure  by  fuel  cut-off. 

V.  Varying  internal  pressure,  by  splitting  the  air  from  the 
compressor  and  sending  more  or  less  of  it  through  or  around 
the  fire. 

.  VI.  Varying  internal  pressure  by  blow-off. 

VII.  Combination  of  varying  initial  pressure  to  power  cyl- 
inder, and  varying  cut-off  to  same. 

VIII.  By  throttling  the  exhaust. 

47.  Preheating  and  regeneration  : 

A  heating  of  the  air  after  compression,  and  before  reaching 
the  fire,  will  insure  a  good  combustion,  and  if  this  is  done  by 
exhausted  heat,  it  aids  the  economy  of  the  engine. 

I.  Causing  the  air  approaching  the  fire  to  first  surround  the 
fire-box  as  a  jacket. 

II.  Causing  exhaust  and  compressed  air  to  pass  on  opposite 
sides  of  a  plate. 

III.  Alternately  sending  fresh  air  and  exhaust  through  the 
same  chamber,  which  must  then  be  present  in  duplicate. 

IV.  Combination  of  exhaust  regenerator  and  fresh  air  fire-box 
jacket. 

48.  Fuel  feed  : 

Coal  may  be  fed  by  any  automatic  stoker,  and  from  above, 
below,  or  the  side  ;  we  will  omit  these. 

I.  Oil  by  gravity,  cut  off  by  internal  pressure. 

II.  Oil  by  pump,  cut  off  by  by-pass. 

III.  Oil  by  water  displacement,  cut  off  by  internal  pressure. 

IV.  Oil  by  injector  suction. 

V.  Gas  by  pump. 

49.  Gas  and  oil  burners  : 

I.  Air  and  gas  fed  from  opposite  openings,  jets  impinging. 
Wilcox,  Reeve. 

II.  Air  and  gas  fed  through  separate  openings,  the  jets  mix- 
ing by  impact  with  platinum  rose.     Villeneure. 

III.  Air  and  gas  mixed,  fed  through  simple  opening.     Bab- 
cock. 


46  THE   HEAT-ENGINE   PROBLEM. 

IV.  Air  and  gas  mixed,  fed  through  gauze  screen.  Brayton, 
Schumm. 

Y.  Air  and  gas  mixed  by  injector  at  burner,  passing  through 
openings  into  larger  chamber,  and  products  through  openings 
similar  to  first,  but  larger  in  area.  Schrnid  and  Beckfeld. 

VI.  Volatile    oil   vaporized   by   heat   of  burner   burning   in 
atmosphere  of  air.     "Wilcox. 

VII.  Volatile  oil  vaporized  by  falling  on  hot  plate  in  atmos- 
phere of  air.     Schmid. 

VIII.  All   kinds   of    oil    sprayed    into    atmosphere   of   air. 
Nordberg  and  Shadall. 

IX.  Volatile  oil  dropped  on  grating,  where  it  meets  air,  the 
mixture  burning  on  one  side.     Brayton,  Wilcox. 

X.  Hot-air  atmosphere  for  an  injection  of  fuel.     Diesel. 
50.  Mixers  and  proportioners  : 

I.  Mix  at  burner,  proportions   maintained  only  by  pump  of 
proper  size. 

II.  Pass  air  through  volatile  oil  kept  at  fixed  temperature  by 
exhaust. 

III.  Mix   at  burner,  proportions   maintained   by   pumps   of 
proper  size,  aided  by  a  device  to  feed  both  pumps  at  constant 
pressure. 

IV.  Proportions  maintained  by  (a)  movable  partition  between 
air  and  gas  receivers,  to  keep  pressures  equal,  and  (b)  proper 
double  valve  at  the  discharge. 

V.  Mix  at  injector,  with  no  special  device,  for  proportioning. 
Position  of  fire : 

I.  Directly  under  piston. 

II.  At  side  of  cylinder;  each  end,  when  double  acting. 

III.  In  separate,  continuously  operated,  highly  heated  cham- 
ber. 

Cycles : 

Nearly  every  cycle  of  operations  can  be  followed.  Engines 
that  take  air  in  one  side  of  the  cylinder  and  send  it  around  to 
the  other  side,  and  those  with  two  pistons  moving  in  different 
directions,  causing  a  change  of  position  of  the  air  only,  will  give 
a  constant-volume  combustion,  and  whether  the  engine  follows, 
Cycle  II.,  HA.,  B,  or  C  will  depend  on  the  amount  of  expansion 
permitted.  Engines  feeding  the  cylinder  with  a  flame  may  have 
a  constant-temperature,  or  constant -pressure  combustion,  de- 
pending on  the  fuel  used ;  hence  III.  or  IV.,  with  all  their  varia- 


THE   HEAT-ENGINE   PROBLEM.  47 

tions,  are  possible.  Those  engines  that  maintain  a  constant 
pressure  in  the  combustion  chamber  will  follow  III.,  or  some  of 
its  variations — which  one,  will  be  determined  largely  by  the  cut- 
off. A  turbine  system  would  follow  III.  most  nearly. 

51.  Of  the  engines  considered,  and  the  much  larger  number 
not  mentioned,  not  one,  except  the  Diesel,  is  on  the  market  to- 
day.    This,  with  some,  would  be  a  sufficient  argument  to  con- 
demn the  whole  system,  but  a  little  study  will  show  that  the 
trouble  is  nearly  always  in  the  same  place,  and  a  little  persever- 
ance is  all  that  is  necessary  to  remedy  the  defect.     Much  more 
difficult  problems  than  this  have  been  solved  successfully,  but 
there  was  first  necessary  a  recognition  of  the  trouble  and  a  good 
reason  for  spending  time  and  money  to  overcome  it. 

The  compressing  of  air  is  no  new  problem,  and  the  using  of 
hot  gases  is  done  every  day  in  thousands  of  horse-power  of  ex- 
plosion engines,  so  that  these  two  parts  of  the  engine  may  be 
considered  solved,  leaving,  as  the  only  doubtful  essential,  the 
fire,  and  here  is  the  seat  of  most  of  the  trouble. 

52.  The  old  engines,  like  Cayley's,  using  coal,  were  found  to 
cut  with  ash,  etc.;  but,  nevertheless,  when  everything  was  right, 
they  ran  and  gave  a  good  account  of  themselves.    In  the  natural 
order  of  things,  Brayton  appeared  with  a  gas  machine.     The  air 
and  gas  were  mixed  in  proper  and  explosive  proportions,  at  the 
compression  intake,  and  sent  through  a  wire  gauze  grating  to  be 
burned  in  the  cylinder.    Clerk  says  of  it : — "  The  engine  worked 
well  and  smoothly ;  the  action  of  the  flame  in  the  cylinder  could 
not  be  distinguished  from  that  of  steam,  it  was  much  within 
control  and  produced  diagrams  similar  to  steam."     The  flame 
grating  of  gauze  was  the  weak  part,  as  an  accidental  piercing  or 
overheating  caused  an  immediate  back  flash  and  stopped  the 
engine.     Brayton  could  not  stop  this,  so  he  tried  a  volatile  oil 
with  compressed  pure  air,  but  his  burner  was  very  crude  and 
resulted  in  a  goodly  soot  deposit.     The  case  seemed  hopeless, 
and  doubly  so  when  Otto  appeared  in  the  field  with  his  success- 
ful engine,  so  Brayton  gave  up. 

Here,  however,  was  a  working  engine  giving  good  results,  both 
in  economy  and  regulation,  needing  only  a  good  burner  to  keep 
it  going. 

53.  The  immediate   success  and  attractive   principle  of  the 
simple  one-cylinder  Otto  has  held  the  attention  of  nearly  all 
from  then  until  to-day.     One  man  there  was  who,  not  only  did 


48  THE   HEAT-ENGINE   PROBLEM. 

turn  aside,  but,  having  turned,  persevered,  and  he  was  rewarded 
by  success — that  was  Diesel.  He  prepared  an  elaborate  plan 
to  imitate  as  nearly  as  possible  the  Carnot  Cycle,  with  its  iso- 
thermal combustion  in  a  cylinder — certainly  a  striking  novelty. 
But  he  did  not  follow  it,  as  the  low  mean  effective  pressure  of  all 
the  Cycles  IV.,  which  he  attempted  to  follow,  necessitated  immense 
machines  for  the  power  produced ;  what  he  did  do  was  to  repro- 
duce the  Brayton  engine  with  another  burner  and  igniter.  His 
hot  compressed  air  did  what  Brayton  could  not  do,  but  in  every- 
thing else  he  was  strictly  Brayton  with  his  Cycle  III.  of  opera- 
tions, which  lie  ultimately  followed.  This  is  one  solution,  then, 
but  not  necessarily  the  best,  as  Diesel  needs  a  very  high 
compression  to  run,  and,  while  this  is  the  reason  for  his  high 
efficiency,  it  makes  a  heavy  machine.  A  little  lower  efficiency, 
with  less  weight,  would  be  very  acceptable,  but  this  would  pre- 
clude the  Diesel  burner. 

54.  A  detailed  study  of  the^combustion  of  gas  and  oil  should 
certainly  lead  to  a  still  further  opening  up  of  this  promising, 
though  neglected,  field  of  engineering.     Produce  a  good  fire  and 
you  must  inevitably  produce  an  improved  Brayton  engine,  and 
this,  in  view  of  what  has  been  said,  is  certainly  a  very  desirable 
end. 

While  combustion,  as  a  purely  chemical  process,  has  formed 
the  subject  of  numerous  papers  and  researches,  leading  to  most 
interesting  theoretical  results  of  great  value  to  physical  chemists, 
not  so  many  have  resulted  in  the  discovery  of  a  new  or  useful 
mode  of  burning  fuels. 

55.  Investigation  long  ago   showed  that  the  oils  undergo  a 
vaporization  before  combustion,  and  that  the  oil  flame  is  really 
an  oil  vapor,  or  gas  flame,  so  that  a  knowledge  of  the  laws  of 
combustion  of  gases  will  give  us  those  of  oil  combustion,  with 
the  exception  of  the  means  of  previously  vaporizing  the  oil.    In 
fact,  the  different  methods  of  burning  oil  now  in  use  vary  chiefly 
in  this  second  respect,  the  means  provided  for  gasifying  the  oil. 
It  would,  therefore,  be  well  to  look  at  the  question  of  gas  com- 
bustion first. 

Gases  burn  by  combining  chemically  atjhigh  temperature  with 
oxygen,*and  the  study  of  their  combustion  may  be  most  readily 
divided  into  classes  whose  characteristics  are  the  ways  in  which 
this  coming  together  of  the  gas  and  its  oxygen^are  provided  for. 

56.  This  leads  to  the  division : 


THE   HEAT-ENGINE   PKOBLEM.  49 

Class  I.  Gas  issuing  from  an  orifice  into  a  supporting  at- 
mosphere and  where  all  the  oxygen  for  combustion  is  derived 
from  that  atmosphere. 

Class  II.  Gas  mixed  with  oxygen  insufficient  in  quantity  for 
its  combustion  or  for  the  formation  of  an  explosive  mixture, 
issuing  into  a  supporting  medium  from  which  all  necessary 
additional  oxygen  is  derived. 

Class  III.  Gas  mixed  with  oxygen  in  quantities  insufficient 
for  complete  combustion,  but  sufficient  for  the  formation  of  an 
explosive  mixture,  issuing  from  an  orifice  into  a  supporting  at- 
mosphere, from  which  all  necessary  additional  oxygen  is  to  be 
derived. 

Class  IV.  Gas  mixed  with  oxygen  in  just  sufficient  quantities 
for  combustion,  issuing  from  an  orifice  into  any  sort  of  atmos- 
phere. We  shall  call  a  mixture  of  this  sort  a  "chemical" 
mixture. 

Class  V.  Gas  mixed  with  oxygen  in  such  quantities  as  to 
form  an  explosive  mixture,  but  with  insufficient  oxygen  for  com- 
plete combustion,  burned  in  a  mass  by  a  single  explosion. 

Class  VI.  Gas  mixed  with  oxygen  in  chemical  proportions, 
burned  by  a  single  explosion  in  mass. 

57.  The  first  class  of  combustion  is  very  imperfect,  conse- 
quently only  low  temperatures  result,  while  large  excesses  of 
oxygen  over  what  is  chemically  necessary  are  required.  It  is 
to  this  very  imperfection  that  we  owe  the  efficiency  of  our  ordi- 
nary gas  jet  as  a  source  of  light.  The  unequal  distances  trav- 
elled by  molecules  of  gas  before  reaching  the  place  where  they 
can  find  and  combine  with  the  necessary  oxygen,  gives  the  flame 
a  volume;  i.e.,  a  certain  portion  of  space  is  filled  with  the  flame. 
In  the  study  of  combustion,  as  the  origin  of  heat,  this  class  is  of 
no  importance.  Mixing  the  oxygen  with  the  gas,  previously  to 
heating  for  ignition,  as  in  Class  II.,  is  a  direct  aid  to  nature, 
eliminating  the  hunting  process  of  Class  I.,  or,  at  any  rate,  re- 
ducing it,  and  making  necessary  only  the  heating  to  the  igni- 
tion temperature  to  cause  combustion.  This  is  shown  in  the 
immediate  shortening  of  the  flame  over  that  of  the  previous 
class,  and  its  loss  of  luminosity,  while  still  retaining  the  vol- 
ume character  of  the  flame.  It  is  the  principle  of  the  Bunsen 
burner,  and  the  large  class  that  follow  it  for  use  in  furnaces, 
heaters,  cooking  stoves,  and  heating  water  in  steam  carriages. 
58.  In  most  of  these  the  mixture  of  air  with  the  fuel  is  made 


50  THE   HEAT-ENGINE   PROBLEM. 

by  causing  the  jet  of  gas  to  impinge  on  a  mass  of  air,  some  of 
which  is  carried  along  with  the  air  under  the  double  influence 
of  gas  friction  and  the  heated  top  of  the  burner,  whence  the 
mixture  issues. 

Some  other  systems,  of  which  the  American  Gas  Furnace 
System  is  one,  effect  the  mixture  in  closed  chambers  before  exit 
at  the  burner. 

Combustion  of  Class  II.  is  characterized  by  the  fact  that 
there  is  an  actual  volume  of  flame  ;  the  flame  is  hotter  than  in 
Class  I.,  which  means  that  for  a  given  flame  volume,  either  more 
gas  is  burned,  or  the  products  of  combustion  are  less  diluted ; 
the  flame  is  less  luminous  and  not  of  uniform  color  throughout 
its  volume. 

An  infinite  variety  of  details  of  arrangement  in  the  exit  and 
mixing  of  the  air  and  gas  may  be  devised  with  varying  results 
for  special  cases,  but  we  may  say  of  all  of  them  that  though  the 
combustion  be  very  perfect  and  the  amount  of  heat  generated 
large,  yet  there  is  always  a  "  flame  volume,"  indicating  a  strug- 
gle, as  it  were,  on  the  part  of  the  gas  and  air  in  their  final  com- 
bustion. The  combustion,  though  approaching  perfection  in 
many  cases,  is  rendered  so  only  by  the  use  of  a  large  excess 
of  the  oxygen  chemically  required  giving  oxidizing  products  of 
combustion. 

59.  It  is  only  when  we  previously  mix  the  gas  and  air  com- 
pletely and  uniformly  in  the  proper  chemical  proportions   that 
we  can  get  non-reducing,  non-oxidizing  products  of  combustion, 
and,  since  none  of  the  heat  goes  to  warm  excesses  of  oxygen  or 
of  fuel,  the  temperature  of  these  products  must  be  the  highest 
possible.     Combustion  of  this  sort  is  flameless,  or,  rather,  what 
flame    there   is   is   without    volume,  having   only   length    and 
breadth  without  thickness,  and  is,  in  fact,  a  surface. 

Such  combustion  is  governed  by  laws  quite  different  from 
those  under  which  the  classes  already  noted  operate,  and  it  is 
to  the  combustion  of  chemical,  and  other  explosive  mixtures, 
that  tliis  section  is  mainly  devoted. 

60.  Let  us  consider  first  the  class  mentioned  as  Class  VI.,  in 
which  a  mass  of   chemical  mixture — i.e.,  gas  and    its   needed 
oxygen — is  confined  in  a  chamber.   If  inflammation  be  provoked 
at  any  point  of  the  mass,  it  will,  by  self-propagation,  finally  and 
successively  inflame   the  whole   mass.     This   is  the   first  and 
fundamental  principle  of  this  sorfc  of  combustion.     The  investi- 


THE   HEAT-ENGINE   PROBLEM.  51 

gation  of  this  propagation  of  inflammation  by  such  men  as  Davy, 
Bunsen,  Mallard  and  LeChatelier,  Berthelot  and  others,  has 
shown  that : 

(a)  In  any  mixture,  the  rate  of  propagation  is  constant  for  a 
given  temperature  before  inflammation. 

(b)  The  rate  of  propagation  for  such  mixtures   varies   with 
different  combustibles,  being,  for  example,  very  fast  for  hydro- 
gen and  slow  for  marsh  gas. 

(c)  The  rate  of  propagation  increases  with  the  temperature  of 
the  mixture  before  inflammation. 

-(d)  The  combustion  is  visible  by  reason  of  a  flame-cap,  or 
deep  blue  film  of  flame,  which  travels  through  the  mass,  and 
which,  at  any  instant,  completely  separates  all  the  burned  from 
the  unburned  mixture. 

This  uniformity  of  velocity  of  inflammation  would  indicate 
that  in  a  mass  where  inflammation  had  started  at  a  point,  the 
flame-cap,  or  surface  of  combustion,  exists  at  any  instant  on  the 
surface  of  a  sphere  whose  radius  is  proportional  to  the  time 
elapsed. 

61.  All  this  has  been  assumed  to  take  place  in  a  large  mass  of 
gas.     If,  however,  the  enclosing  vessel  be  given  special  forms, 
certain  other  characteristics  are  brought  out.     One  which  is  of 
interest  to  us  is  the  fact  that,  when  the  enclosing  vessel  is  a  cyl- 
inder, or  prism,  in  which  the  combustion  surface  travels  with  its 
centre  on  the  axis,  the  velocity  becomes  affected  by  reduction  of 
cross-section  and  that  there  will  always  exist  for  every  such  mix- 
ture an  area  of  cross-section  so  small  that  the  self-propagation 
ceases.     This  has  been  explained  by  saying  that  the  walls  car- 
ried off  heat  so  fast  that  the  small  flame-cap  could  not  generate 
heat  enough  to  keep  itself  above  the  temperature  of  ignition. 
Davy  secured  the  same  effect  by  using  his  screen  of  wire  gauze, 
which,  if  interposed  in  the  path  of  the  combustion  surface,  in- 
stantly cooled  the  same  sufficiently  to  prevent  the  ignition  of 
the  mixture  on  the  other  side,  provided,  of  course,  the  tempera- 
ture of  the  gauze  itself  is  sufficiently  low. 

62.  When  a  neutral  diluent  gas,  such  as  N  or  CO2,  is  added 
to  a  chemical  mixture  arranged  for  the  above-discussed  com- . 
bustion,  its  effect  is  to  reduce  the  rate  of  propagation,  though 
not  in  conformity  with  any  law  yet  discovered.     Of  course,  there 
will  be  a  point  when  so  much  of  the  neutral  gas  is   present 
that  combustion  is  impossible,  but  no  reliable  data  are  at  hand 


52  THE   HEAT-ENGINE   PROBLEM. 

on  this  point,  as  the  same  conditions  often  give  widely  varying 
results. 

While  large  quantities  of  a  neutral  gas  may  be  added,  with- 
out affecting  the  combustion  except  to  decrease  the  rate  of  prop- 
agation, a  dilution  by  a  comparatively  slight  amount  (  f  oxygen 
will  prevent  it  altogether.  An  excess  of  ga  ,  it  has  been  found, 
will  act  within  certain  limits  like  the  presence  of  a  neutral  gas. 
By  far  larger  amounts  of  fuel  than  of  oxygen  may  be  present  in 
excess  without  arresting  combustion. 

63.  This  brings  us  to  class  V.,  where  explosive  mixtures  are 
burned  in  mass,  the  mixtures  having  excess  of  fuel.     The  com- 
bustion is  possible  within  quite  wide  limits,  with  no  other  effect 
than  varying  the  rate  of  propagation.     In  fact,  we  see  a  great 
deal  of  it  to-day  in  our  gas  engines.  While,  of  course,  we  should, 
in  these  engines,  invariably  use  the  proper  chemical  mixture,  they 
are  seldom,  if  ever,  constructed  to  maintain  this  properly,  and,  as 
a  slight  excess  of  oxygen  will  completely  prevent  inflammation, 
the  error  is  always  made  on  the  other  side  ;  sooty  exhausts  bear 
testimony  to  this.    The  gas  engine  also  gives  evidence  of  the  fact 
that  neutral  gases  decrease  the  rate  of  propagation,  for  in  some 
two-cycle  engines  which  I  have  lately  examined  I  find  it  im- 
possible to  get  a  vertical  combustion  line  on  the  indicator  dia- 
gram with  a  fixed  ignition,  except  at  very  slow  speeds — about  60 
revolutions  per  minute.     This  is  due  entirely  to  the  presence 
of  exhaust  gases  in  excessive  quantities  as  diluents  to  the  charge. 

Some  of  the  principles  above  noted  as  belonging  to  masses  of 
mixture  at  rest  will  make  clearer  the  nature  of  the  problem  of 
combustion  of  the  same  mixtures  when  in  motion  issuing  from 
an  orifice.  x 

64.  The  desirability  of  being  able  to  burn  an  explosive  mix- 
ture continuously  and  non-explosively  under  commercial,  rather 
than  laboratory,  conditions  having  long  been  obvious,  a  series  of 
experiments  was  undertaken  at  Columbia  University  with  this 
end  in  view.     Many  experiments  were  made  and  various  results 
obtained,  but  as  a  full  account  would  take  too  much  space  and 
avail  little,  only  a  few  characteristic  experiments  will  be  noted 
as  leading  up  to  the  result.      Consider  a  mass  of  explosive  mix- 
ture passing  through  a  non-conducting  tube  with  a  uniform  ve- 
locity v.     Then,  if  inflammation  be  started  at  some  point,  the  sur- 
face of  combustion  may  remain  at  rest  or  move  with  or  against 
the  current.    J>enate  .the  rate  of  propagation  by  r.     Then,  when 


THE   HEAT-ENGINE    PEOBLEM.  53 

•v  >'  r  the  surface  of  combustion  will  move  with  the  current,  and 
if  the  tube  has  an  end,  the  flame  will  "  blow  off"  and  combustion 
cease ;  if  v  —  r  the  surface  of  combustion  will  remain  at  rest, 
other  influences  being  inoperative ;  if  v  <  r,  the  surface  of  com- 
bustion will  move  back  toward  the  source  or  "  back  flash." 

Of  course,  a  small  tube  of  heat-conducting  material  will  exert 
considerable  cooling  effect,  but  for  the  present  we  will  not  con- 
sider such  tubes. 

In  a  practicable  system  of  burning  an  explosive  mixture  con- 
tinuously, we  may  state  the  following  as  desiderata  and  later  see 
ht>w  they  can  be  secured. 

I.  "Back  flashing  '  must  be  prevented. 

II.  "Blow  off"  must  be  prevented. 

III.  Combustion  surface  must  be  localized. 

IV.  It  must  remain  localized  for  wide  ranges  of  feed  or  veloc- 
ity of  flow  of  the  mixture. 

V.  The  localization  must  be  unaffected  by  changes   of  tem- 
perature. 

VI.  Large  or  small  quantities  must  be  burned  without  affect- 
ing the  above,  and  the  transition  from  very  small  quantities  to 
very  large,  or  vice  versa,  however  sudden,  should  be  easy. 

65.  The    first  requirement  might  be  accomplished    in  three 
ways  : 

(ft)  By  using  a  long  tube  of  some  conducting  material  and 
so  small  in  diameter  as  to  prevent  the  passage  of  the  flame-cap 
under  any  circumstances. 

(b)  By  using  wire  gauze  screens. 

(a)  By  causing  the  mixture  to  flow  at  some  point  with  a 
velocity  always  greater  than  the  rate  of  propagation. 

The  first  (a)  is  impracticable,  as  it  permits  of  only  small  quan- 
tities being  burned  ;  the  second  (b)  will  not  work  when  the  wire 
gauze  gets  hot ;  this  leaves  (<?),  which  is  practicable,  as  a  valve  in 
a  pipe  will  answer  for  the  necessary  contraction  and  consequent 
increase  of  velocity.  Hence  we  must  put  down  as  the  first  re- 
quirement in  our  desired  method  of  combustion  the  following. 
At  some  point  before  the  combustion  surface  is  reached  the  ve- 
locity of  feed  must  be  such  that  v  >  r. 

66.  Requirement  II.  might  be  accomplished  in  three  ways  :  - 

(a)  By  so  reducing  the  velocity  after  passing  the  high-speed 
point  that  we  have  at  some  surface  v  =  r. 

(b)  By  suddenly  increasing  the  temperature  of  the  mixture  so 


54  THE   HEAT-ENGINE   PltOBLEM. 

as  to  increase  the  rate  of  propagation  while  v  remains  con- 
stant ;  or, 

(c)  By  both  reducing  v,  by  spreading  the  current,  and  in- 
creasing r  by  heating. 

All  of  these  ways  are  practicable ;  but,  as  a  reduction  of 
velocity  alone,  or  a  sufficient  heating  alone  would  not  produce 
the  desired  results  so  well  as  both  operating  together,  there  was 
introduced  as  the  second  requirement  in  our  desired  method, 
the  following.  After  passing  the  point  where  v  >  r,  the  ve- 
locity of  the  mixture  should  be  so  reduced  and  its  temperature 
increased  as  to  make  v  l  =  r1. 

67.  With  these  conditions  in  mind,  let  us  consider  an  experi- 
ment.    Let  the  mixture  issue  from  an  orifice  into  the  air.     By 
properly  regulating  the  velocity  of  exit,  the  flame-cap  can  be 
maintained  at  the  orifice — the  only  device  with  which  I  suc- 
ceeded in  this  experiment  was  by  causing  water  to  drip  into  the 
supply  chamber ;  the  position  of  the  flame-cap  is  so  extremely 
sensitive  to  changes  of  flow  that  all  other  methods  which  were 
tried  for  obtaining  a  constant  velocity  of  exit,  variable  at  will, 
failed — increase  the  flow  slightly,  and  the  flame-cap  will  lift  off. 
This  may  be  done  until  the  flame-cap  is  as  much  as  2  inches 
(with  illuminating  gas  and  air)  from  the  orifice  before  extinction 
takes  place.     It  would  seem  that  the  impinging  of  the  jet  on  the 
atmosphere  should  spread  it  and  so  reduce  its  velocity,  but  no 
appreciable  increase  of  diameter  could  be  observed.     When  the 
cap  is  close  to  the  orifice,  it  is  of  a  deep  blue  color,  uniform  in 
shade  over  the  disk,  and  the  edges  are  sharply  defined  ;  whereas, 
as  it  lifts  off  some  distance,  it  becomes  indistinct  and  unsteady 
at  the  edges  until,  at  the  moment  of  extinction,  it  fades  into 
nothing.     When  the  cap  is  away  from  the  orifice,  while  there 
is  no  visible  connection  with  the  source  of  supply,  there  really 
exists  a  column  of  mixture  extending  from  the  orifice  to  the  cap 
and  passing  through  the  atmosphere.     Naturally,  at  the  surface 
of   this  column,  diffusion  will  take  place,   and  the  longer  the 
column,  the  greater  will  be  this  diffusion  effect,  thus  affecting 
the  composition  of  the  advancing  column  of  mixture  and  caus- 
ing partial  loss  of  gas.     This  is  the  real  cause  of  extinction. 

68.  From  these  experiments  we  can  draw  the  conclusion  that 
the  current  cannot  be  sufficiently  reduced  in  velocity  by  issuing 
into   an  atmosphere  of  lower  pressure  to   prevent  "  blow-off " 
before  diffusion  with  the  atmosphere  so  alters  the  character  of 


THE   HEAT-ENGINE   PROBLEM. 


55 


the  mixture  as  to  cause  extinction  before  reaching  the  surface 
of  combustion.  This  calls  for  a  new  condition  besides  those 
noted  in  the  requirements  for  combustion.  The  reduction  of 
velocity  of  the  mixture,  after  passing  the  place  where  v  >  r, 
must  be  accomplished  in  such  a  way  as  to  prevent  diffusion 
with  any  other  gas. 

69.  To  prevent  this  diffusion,  there  naturally  suggests  itself 
the  expedient  of  surrounding  the  issuing  jet  with  a  shield  of 
larger  diameter,  to  still  permit  of  the  desired  expansion.  This 
is  shown  in  Fig.  47,  and  is  essentially  the  same  as  proposed  by 
Ladd,  Schmid,  Beckfeld,  and  others.  The  mixture  must  issue 
from  orifice  a  with  a  velocity  va  >  r  ;  this  will  prevent  "  back 
flash."  If  the  distance  from  a  to  b  is  long  enough  to  allow  the 
gas  to  spread  and  reduce  velocity,  "  blow-off "  will  not  occur 
until  vb  >  r,  and  within  these  limits  the  flame-cap  should  re- 


FIG.  47. 

main  within  the  shield.  A  trial  shows  that  when  (Dia)b  is  but 
slightly  larger  than  (Dia)  a>  the  feed  velocity  may  be  varied  in 
about  the  proportions  noted,  but  this  means  that  we  are  confined 
within  very  narrow  working  limits.  The  flame-cap  seems  to 
lose  its  flat,  volumeless  character  for  some  reason  not  at  first 
clear.  When  (Dia)b  is  much  larger,  say  four  or  five  times 
(Dia)ai  a  slow  increase  of  feed  velocity  above  r  reveals  the  ad- 
vancing flame-cap  just  as  if  the  shield  were  not  there.  Later,  a 
slight  spreading  is  noted,  and  then  the  flame  actually  begins  to 
show  volume,  as  if  there  were  no  longer  an  explosive  mixture 
present ;  this  heats  up  the  shield.  A  little  consideration  will 
show  this  to  be  due  to  the  diffusion  of  the  advancing  and 
slightly  spreading  column  with  the  products  of  combustion 
within  the  shield,  and  the  high  temperature  of  the  shield  helps 
to  maintain  a  combustion  of  what  is  now  a  diluted  explosive 
mixture  beyond  a  point  where  that  combustion  would  be  pos- 
sible if  cold.  An  increase  of  velocity  will  cause  extinction  by 
"blow-off." 


56  THE   HEAT-ENGINE   PROBLEM. 

70.  Here  the  results  are  somewhat  better  than  in  the  last 
case  without  the  shield.  The  principles  operating,  with  the 
results  are  :  back  flash  prevented  by  sufficiently  great  initial 
velocity  at  a ;  a  spreading  to  reduce  velocity,  but  very  slight 
and  insufficient,  as  proved  by  the  narrow  working  limits ;  diffu- 
sion is  not  prevented ;  gas  is  partly  heated  before  burning  by 
the  shield,  which  helps  to  continue  combustion.  If  the  advanc- 
ing column  did  increase  in  cross-section  and  decrease  in  velocity 
while  advancing,  successive  possible,  positions  of  the  flame- cap 
would  be  as  shown  at  1,  2,  3,  4,  etc.,  of  Fig.  47. 

It  is  obvious  that  at  any  point  between  a  and  7,  such  as  4, 
the  cap  is  surrounded  by  products  of  combustion,  and  the 
advancing  column  of  mixture  is  passing  through  an  atmosphere 
chiefly  composed  of  the  same,  resulting  in  disastrous  diffusion. 


FIG.  48. 

This  at  once  suggests  giving  the  shielding  envelope  the  form  of 
a  cone,  supposing  the  orifice  circular,  so  that  the  flame-cap  at 
any  instant  may  entirely  fill  up  the  space  between  the  walls. 

71.  Apparatus  with  this  end  in  view  was  tried  and  gave  some 
interesting  results.  Fig.  48  shows  a  cone  of  45  degrees  angle, 
with  a  ^-inch  orifice  such  as  was  used.  The  velocity  of  feed  was 
so  adjusted  as  to  cause  the  flame-cap  to  advance  slowly  from  a, 
with  the  expectation  stated  above.  The  flame-caps  at  successive 
positions  took  the  forms  shown  at  the  lines  1,  2,  3,  4,  5,  6,  etc., 
and  finally  "blow-off"  occurred.  Since  the  only  place  where  the 
combustion  surface  can  remain  at  rest  is  on  a  surface  where 
v  =  r,  and  since,  secondly,  r  is  here  constant,  the  curves  indi- 
cating the  intersection  of  the  combustion  surfaces  by  meridian 
planes,  give  us  graphical  values  of  the  velocity  of  the  advan- 
cing column  of  mixture.  It  is  seen  that  the  expected  spreading 
did  not  take  place,  and  that  at  any  circular  cross-section  of  the 


THE    HEAT-ENGINE   PROBLEM.  57 

cone,  the  velocity  was  greatest  at  the  centre,  decreasing  toward 
the  edges. 

The  curves  1,  2,  3,  etc.,  are  really  cross-sections  of  successive 
constant  velocity  surfaces  in  the  advancing  column,  and  the 
surface  of  combustion  will  lie  on  that  surface  of  constant-trans- 
mission velocity  where  v  =  r. 

72.  A  constant-velocity  surface  may  be  defined  as  a  surface  at 
every  point  of  which  the  moving  particles  of  gas  have  equal  in- 
stantaneous velocities.   If  these  successive  surfaces  had  remained 
flat  or  nearly  so,  the  proper  sort  of  spreading  of  current  and 
uniform  decrease  of  velocity  would  be  indicated.     This  gives  us 
an  accurate  definition  of  how  we  want  our  velocity  reduced  after 
passing  the  point  where  v  >  r.     The  velocity  of  the  advancing 
mixture  must  be  reduced  without  diffusion,  so  as  to  keep  the 
surfaces  of  constant  velocity  of  such  form  that  adjacent  points 
on  any  one  will  be  at  approximately  the  same  distance  from  the 
point  where  spreading  begins.     Reducing  the  angle  of  the  cone, 
while  helping  matters  considerably,  reduces  the  range  of  feed 
velocities  within  impracticable  limits. 

73.  Many  ways  of  bringing  about  the  above  were  tried,  but 
only   one   seemed  preeminently   good   both   by   reason   of  its 
simplicity  and  effectiveness,  for  it  fulfils  almost  perfectly  the 
requirements  proposed  for  our  desired  method ;  this  is,  to  fill 
the  cone  with  fragments  of  refractory  material  such  as  pottery, 
broken  crucibles,  bits  of  magnesite,  or  any  other  rock  that  will 
stand  the    high   temperature  without   fusing.     In  cones  of  60 
degrees,  and  with  a  ^-inch  orifice,  I  have  found  pieces  about 
|  inch  diameter  to  answer  well. 

These  separate  pieces  of  solid  matter  interpose  many  reflect- 
ing surfaces  without  materially  hindering  the  advance  of  the 
mixture,  and  cause  it  to  spread  in  the  way  desired,  keeping  the 
surface  of  combustion  spherical  and  preventing  diffusion.  A 
variation  of  velocity  causes  the  spherical  surface  of  combustion 
to  vary  only  in  diameter,  and  the  limits  of  feed  are  determined 
only  by  the  size  of  the  cone. 

74.  A  cone  of  given  altitude  will  give  the  greatest  range  of 
variation  of  diameter  of  cross-section  when  its  angle  is  180  de- 
grees. This  is  a  plane  surface  which,  with  the  orifice  and  broken 
rock,  should  appear  as  in  Fig.  49.     Here  the  surface  of  com- 
bustion is  approximately  a  semi-sphere.     Trial  shows  that  tbis 
arrangement  works  perfectly,  and  the  limits  of  feed  are  deter- 


58 


THE   HEAT-ENGINE   PROBLEM. 


mined  only  by  the  size  of  the  pile  of  rock  surrounding  the  open- 
ing. A  cone  of  360  degrees,  or  no  cone  at  all,  suggests  the 
surrounding  of  the  nozzle  by  broken  rock  without  any  enclosing 
walls  (Fig.  50).  This  arrangement  also  works  remarkably  well. 


FIG.  49. 

The  surface  of  combustion  is  here  approximately  a  sphere, 
giving  the  greatest  possible  increase  in  area  of  the  surface  of 
combustion  for  the  distance  travelled  from  the  nozzle. 

If  d  denote  the  distance  from  the  point  where  spreading 
begins  to  the  surface  of  combustion  and  S  the  area  of  the  sur- 
face, we  have : 


For  a  cone, 


—  7id~  tan  2  of. 


For  no  walls  (Fig.  50),  Sl  = 


FIG.  50. 


75.  Not  only  is  the  greatest  possible  range  of  action  by  veloc- 
ity reduction  thus  obtained,  enabling  the  greatest  possible 
amount  of  mixture  to  be  burned  in  a  given  volume,  but  this 


THE   HEAT-ENGINE   PROBLEM.  59 

amount  is  further  augmented  by  reason  of  the  increase  of  the 
rate  of  propagation  caused  by  the  passage  of  the  mixture 
between  the  hot  fragments.  Hence  both  principles  operate 
simultaneously  toward  the  desired  end. 

We  have  thus  arrived  at  a  method  of  continuously  burning 
explosive  mixtures  of  all  sorts,  whether  in  the  chemical  propor- 
tion or  not,  as  classified  in  IY.  and  V. 

76.  The  method  fulfils  all  the  conditions  set  down  as  neces- 
sary, and  may  be  stated  as  follows  : 

I.  Cause  the  mixture  to  pass  a  point  where  its  velocity  of 
transmission  shall  be  always  greater  than  the  rate  of  propaga- 
tion of  inflammation  through  the  mixture.     This  may  be  done 
by  a  valve  in  the  feed-pipe. 

II.  So  spread  the  current  of  mixture  after  it  passes  this  point 
of  high  velocity  that  surfaces  of  constant-transmission  velocity 
shall  be  of  such  form  as  to  keep  adjacent  points  on  any  one  at 
approximately  the  same  distance  from  the  point  where  spread- 
ing begins.     The  whole  spreading  must  take  place  so  that  the 
advancing  unburned  mixture  cannot  diffuse  with  any  other  gas. 
This    can   be    accomplished   by   surrounding   the    orifice   with 
solid  fragments,  introducing  numerous  reflecting  surfaces  which 
accomplish  the  spreading;    also,  by  the  passage  through  the 
interstices  between  this  solid  matter,  the  mixture  is  heated  and 
the  rate  of  propagation  increased,  making  possible  the  burning 
of  more  mixture  in  unit  volume. 

77.  When  a  chemical  proportion  is  maintained  in  the  mixture, 
all  the  combustion  takes  place  on  the  combustion  surface,  giving 
absolutely  neutral  products  of  combustion ;  but  when  an  excess 
of  gas  is  present  within  certain  limits,  all  gas  that  can  find 
oxygen  burns  explosively  between  the  solids,  while  the  excess 
acts  merely  as  a  neutral  diluent  to  be  burned  when  it  meets  an 
oxygen  atmosphere  later  on.     By  properly  placing  the  oxygen 
atmosphere  to  burn  the  excess  gas,  we  can  get  the  hot  products 
either  reducing  or  oxidizing — reducing  after  leaving  the  explosive- 
combustion  surface  and  before  meeting  the  excess  of  oxygen  in 
the  atmosphere,  oxidizing  after  that  meeting. 

It  might  be  here  noted  that  the  principle  well  known  in  explo- 
sive combustion  at  constant  volume,  and  constantly  operating 
in  the  gas  engine,  that  "  to  a  chemical  mixture  of  air  and  gas 
there  may  be  added  large  quantities  of  gas  without  altering 
the  explosive  properties  of  the  mixture,"  is,  by  these  experi- 


CO  THE   HEAT-ENGINE   PROBLFM. 

ments,  extended.  It  appears  that  in  explosive  combustion  at 
constant  pressure,  or,  as  I  have  called  it,  "  continuous  combus- 
tion of  explosive  mixtures,"  the  same  principle  applies,  and, 
though  no  real  proportion  measurements  have  yet  been  made, 
it  seems  to  a  wider  degree.  That  is  to  say,  that  in  the  method 
here  described,  mixtures  of  air  and  gas,  with  gas  in  excess  of 
the  amount  the  air  present  can  support,  will  burn  explosively. 
The  excess  gas  present  acts  merely  as  a  neutral  diluent,  such 
as  the  nitrogen  of  the  air.  It  is  a  fact  also  that,  as  the  solid 
fragments  heat  up,  the  excess  may  be  greater  than  when  they 
are  cold. 

78.  Another  interesting  thing  noted  in  these  experiments  is 
that  an  explosive  fire  will  sometimes  emit  a  musical  note  ;  it 
may  be  that  this  is  always  true  and  that  its  absence  at  any  time 
is  due  to  lack  of  the  proper  resonator.     This  would  seem  to 
indicate  that  what  to  the  eye  appears  as  continuous  combustion, 
is  only  approaching  the  limit,  which  is  continuity,  and  that  in 
reality  single  explosions  in  rapid  and  reyular  succession  are 
taking  place.      It  would  be  interesting  to  determine  whether 
the  temperature  or  kind  of  gas  has  any  influence  on  this  note. 

79.  The  perfection  of  the  gas  combustion  above  discussed  and 
the  simplicity  of  the  apparatus  make  the  method  highly  satis- 
factory, and  the  solution  of  the  difficult  problem  of  explosive- 
gas  combustion  lends  encouragement  to  the  even  more  diffi- 
cult case  of  oil  combustion.     The  experiments  with  oil,  though 
not  yet  complete,  promise  to  give   equally  satisfactory  results  ; 
in  fact,  it  is  almost  certain  that  they  will.     However,  the   oil 
system  has  so  far  been  tried  in  only  a  few  cases,  and  it  is  not 
wise  to  announce  the  complete  success  of  the  system  until  all 
possible  conditions  have  been  met. 

80.  It  was  shown  that  there  were  only  two  classes  of  com- 
bustion worthy  of  consideration  for  use  in  internal-combustion 
engines,  and  only  two  cycles  that  promised  returns  commen- 
surate with  the  labor  and  time  that  might  be  expended  in  their 
development — the  Otto  and  the  Brayton.     The  Otto  is  simple 
to  carry  out  in  practice,  and  is  now,  to  all  intents  and  purposes, 
fully  developed,  while  the  Brayton  has  hitherto  failed,  chiefly 
because  of  the  difficulty  of  handling  explosive  mixtures  in  the 
dsireed  way.     This  difficulty  now  removed,  puts  the  Brayton 
cycle  on  a  different  basis,  making  the  system  quite  as  feasible 
as  the  Otto,  and,  in  most  respects,  promising  better  results.   Not 


THE   HEAT-ENGINE   PROBLEM.  61 

only  this,  but  the  fact  that  the  oil  combustion  will  almost  cer- 
tainly be  put  within  as  easy  reach,  adds  another  point  in  favor 
of  the  Brayton  cycle,  in  the  carrying  out  of  which  any  sort  of 
oil  may  be  used,  whereas  the  Otto  is  here  barred. 

It  is  not  necessary  to  enumerate  here  the  comparative  merits 
of  the  two  systems,  for  that  can  be  easily  judged  by  what  has 
already  been  stated. 

81.  There  is  one  point,  however,  that  should  receive  notice, 
that  is,  should  we  operate  Brayton  cycles  with  intermittent  or 
continuous  combustion  ?  With  intermittent  combustion  the  fire 
burns  within  the  cylinder,  and  as  nothing,  but  fuel  and  air  pass 
the  inlet  valves,  they  can  be  the  more  easily  kept  cool ;  while, 
on  the  other  hand,  the  placing  of  the  burner  beyond  the  valve 
presents  two  undesirable  features  :  first,  the  clearance  must  be 
unusually  large ;  and  second,  the  intermittent  feed  and  cut-off 
of  air  and  fuel  at  just  the  right  time,  without  alteration  of  pro- 
portion in  a  fraction  of  a  second,  introduces  a  condition  very 
difficult  to  meet.  Continuous  combustion  within  a  fire-box  is 
easier  to  handle,  there  being  no  alterations  of  feed  and  the 
clearance  may  be  as  small  as  we  please,  whereas  we  have  as 
undesirable  the  feeding  of  hot  gases  past  the  inlet  valves. 

Which  of  these  alternatives  will  prove  the  better  for  use,  in 
the  system  of  engines  under  treatment,  can  be  decided  only  by 
actual  construction,  but  as  either  will  work,  there  is  no  great 
risk  involved  in  building. 


The  paper  on  liquid  fuel  combustion  which  follows  belongs  prop- 
erly in  the  body  of  the  previous  paper  and  should  follow  other 
matter  of  paragraph  79  page  60,*  but  at  the  time  this  was  written 
the  work  on  oil  had  not  yet  been  completed.  The  slight  lack  of 
continuity  also  which  is  apparent  as  well  as  some  repetition  is  due 
to  the  way  in  which  it  was  found  necessary  to  present  this  some- 
what extended  work,  i.  e.  the  preparation  of  separate  papers  dealing 
each  with  one  phase  of  the  work  but  each  sufficiently  complete 
within  itself  to  make  good  reading  and  hold  the  interest  to  but  one 
topic.  With  this  in  mind  it  is  believed  that  the  connection  and 
interrelation  existing  will  not  seem  too  strained. 

*A.  S.  M.  E.,  Dec.,  1901. 


g This  paper  is  sent  to  you  that  you  may  examine  it  in  advance  of  the 

meeting,  and  prepare  any  discussion  of  it  which  you  may  wish  to  present. 

It  is  issued  to  the  membership  in  confidence,  and  with  the  distinct  understand- 
ing that  it  is  not  to  be  given  to  the  press  or  to  the  public  until  after  it  has  been 
presented  at  the  meeting. 

The  Society  as  a  body  is  not  responsible  for  the  statements  of  fact  or  opinion 
advanced  in  papers  or  discussion.  (Art.  44  of  its  Rules.) 

As  there  will  be  no  adequate  supply  of  extra  copies,  and  papers  are  liable  to 
be  read  by  abstract  only,  preserve  this  copy  for  your  use,  and 

BRING  THIS  COPY  WITH  YOU  TO  THE   MEETING. 

(Subject  to  Revision.) 

Hio.  0934.* 

LIQUID  FUEL    COMBUSTION. 

BY  CHARLES  E.  LUCRE,  NEW  YORK. 

(Non-Member.) 

PRESENTED  BY  R.   H.   FERNALD,   NEW  YORK. 

(Associate  Member  of  the  Society.) 

1.  OIL  combustion,  considered  as  a  rather  complicated  series  of 
physical  actions,  has  never  received  the  attention  due  to  its  impor- 
tance.   There  have  appeared  from  time  to  time  men  who,  taking 
up  the  corresponding  question  for  gases,  gave  to  the  world  a  series 
of  researches  which  leave  but  little  to  be  desired,  and  the  very 
perfection  and  elasticity  of  our  methods  of  burning  gases  brings 
into  stronger  relief  the  narrow  limits  of  present  practice  in  oil 
combustion.     Before  we  can  hope  to  design  special  and  proper 
furnaces  this  problem  must  be  attacked  from  this  standpoint,  and 
the  physical  operations  will  when  brought  together  and  classified 
give  us  the  principles  of  oil  combustion.      A  detailed  and  minute 
treatment  of  this  question  would  call  for  a  lifetime  of  study,  but 
some  of  the  principles  are  more  prominent  and  appear  more 
evident  than  the  others;  a  few  of  these  have  appeared  in  the 
course  of    some  experiments   undertaken   for  an   object  noted 
later. 

2.  The  analytical  treatment  of  the  combustion  of  gases  greatly 
simplifies  the  problem  of  oil  combustion.     By  classifying  the  gas- 
burning  methods  according  to  the  mode  of  bringing  the  air  and 
gas  together,  it  was  found  that  there  were,  broadly,  two  great 

*  To  be  presented  at  the  Boston  meeting  (May,  1902)  of  the  American  Society  of 
Mechanical  Engineers,  and  forming  part  of  Volume  XXIII.  of  the  Transactions. 


2  LIQUID   FUEL   COMBUSTION. 

divisions  of  all  systems,  those  in  which  a  supporting  atmosphere 
was  necessary,  and  those  in  which,  because  of  the  self-propagation  or 
explosive  property  of  the  burning  mass,  no  supporting  atmosphere 
was  necessary.  Moreover  a  distinctly  different  set  of  laws  of 
physical  action  holds  in  each  case.  The  laws  of  combustion  for 
explosive  mixtures  with  their  volumeless  flames  are  radically 
different  from  those  for  all  other  mixtures  the  combustion  of 
which  calls  for  a  supporting  atmosphere,  giving  rise  to  a  volume 
of  flame  due  to  the  meeting  of  the  fuel  and  oxygen  at  different 
points,  and  at  each  springing  into  flame  when  juncture  is  effected. 
The  volumeless  flame  of  the  true  explosive  fire  depends  for  its 
localization  and  maintenance  on  the  relation  between  the  rate  of 
propagation  of  inflammation  in  the  mixtures  and  the  velocity  of 
translation,  together  with  the  extent  of  freedom  from  diffusion 
of  the  fresh  mixture  with  the  products  while  approaching  the 
combustion  surface. 

3.  For  .a  comprehension  of  the  different  cases  of  oil  burning, 
we  must  add  to  our  knowledge  of  gas  combustion  something  on 
the  vaporization  of  the  oils,  since  it  is  conceded  that  oil  will  not 
burn  as  such  a  distillation  or  vaporization  preceding  the  actual 
combination  with  oxygen.    So  that  different  oil  systems  will  differ 
chiefly  in   the   method  of  producing  the  oil  vapor,  and  in  the 
method  of  causing  a  meeting  of  this  vapor  with  the  air.     Any 
two  systems  which  agree  in  these  two  points  must  be  brought 
together  as  coming  under  one  class,  but  perhaps  differing  in  details 
which  may  or  may  not  be  essential  to  good  results. 

4.  Of  all  the  different  systems  proposed  we  can,  according  to 
the  above,  note  only  three  different  general  classes  : 

I.  The  burning  of  oil  in  an  atmosphere  without  previous  treat- 
ment by  air  or  heat.  This  class  burns  the  oil  (a)  from  a  surface 
either  that  of  the  liquid  mass  or  that  of  films  artificially  produced 
by  sand,  stones,  fibrous  or  metal  wicks.  The  vapor  burns  imme- 
diately as  formed,  and  hence  there  can  be  no  mixing  with  air,  the 
flame  existing  merely  in  an  atmosphere  which  may  be  often 
renewed  or  not,  i.e.,  depend  on  blowers  or  mere  convection.  The 
fires  resulting  from  this  class  are  grouped  for  action  and  effects 
with  the  first  kind  of  gas  combustion,  a  jet  of  gas  issuing  unmixed 
into  an  atmosphere  of  air. 

There  may  also  be  included  (b)  those  retort  or  (c)  spray  vapor 
producers  which  deliver  oil  gas,  as  just  noted. 

Oil  burning  by  methods  coming  under  this  class  must  be  subject 


LIQUID   FUEL  COMBUSTION. 

to  the  same  merits  and  defects  as  the  gas  combustion  noted,  how- 
ever diverse,  complicated,  or  ingenious  the  details  of  operation  or 
construction  may  be. 

II.  Under  this  class  will  be  grouped  all  oil  fires  capable  of 
producing   what  is  known  in  gas  combustion  as  the  "Bunsen 
effects."     That  is  to  say,  the  oil  is  vaporized  in  such  a  way  as  to 
permit  the  mixture  with  it  of  a  certain  amount  of  air  before  it 
reaches  the  existing  flame,  and  having  reached  the  existing  flame 
requires  an  oxygen  atmosphere  to  support  combustion. 

Any  system  producing  vapor  which  can  be  handled  as  can  a 
gas  may  also  be  included. 

III.  The  third  class  of  oil  combustion  will  include  all  those 
methods  in  which  the  oil  is  vaporized  and  mixed  with  air  in  such 
proportions  and  in  such  manner  that  there  will  result  an  explosive 
mixture  of  oil  vapor  and  air.     Such  oil  fires  will  be  subject  to  the 
laws  of  combustion  of  explosive  mixtures.     The  vapor  may  be 
produced  in  retorts  by  boiling  a  mass  of  liquid,  or  by  spraying  oil 
on  hot  surfaces  and  then  conducting  it  to  a  point  where  it  may 
mix  with  air,  or  the  oil  may  vaporize  by  contact  with  or  approach 
to  a  hot  surface  in  the  presence  of  the  air. 

5.  The  most  natural  and  earliest  practical  method  of  oil  burn- 
ing was  that  of  simply  lighting  the  surface  of  a  mass  resting  in 
a  pan.  The  amount  of  heat  that  could  be  developed  depending 
on  the  surface  of  oil  exposed  led  to  a  spreading  of  the  oil  over 
plates  and  running  over  numerous  grooves  and  in  the  formation 
of  cascades,  etc.  The  high  flash  point  of  some  oils,  i.e.,  the  high 
temperature  at  which  they  give  off  combustible  vapor  and  the 
presence  of  the  liquid  mass  made  it  impossible  to  burn  them  in 
this  way,  and  hence  was  brought  about  one  of  the  first  improve- 
ments in  oil  combustion.  The  wick  system  results  from  a  desire 
to  produce  more  vapor,  and  this  from  oils  of  high  flash  point ;  by 
it  oil  is  caused  to  spread  out  over  a  large  surface  in  as  thin  a  film 
as  possible,  and  is  then  subjected  to  heat.  Being  in  a  thin  film  it 
is  easily  vaporized  because  of  the  small  quantity  at  any  point  and 
the  ease  with  which  the  substance  supporting  the  film  can  be 
heated  and  kept  hot,  the  vapor  thus  produced  burns  as  it  appears 
in  an  air  atmosphere. 

When  the  film  bearer  has  a4ow  specific  head  the  vaporization  is 
the  more  rapid  at  the  surface  but  slower  beyond ;  with  a  metal 
film  bearer  the  conduction  of  heat  beyond  the  surface  causes  a 
vaporization  at  more  points  and  insures  more  complete  vaporiza- 


LIQUID   FUEL   COMBUSTION. 

tion  by  a  superheating  at  the  surface ;  the  superheating  may  even 
decompose  the  vapor. 

6.  These  wick  burners  are  easily  illustrated  by  a  pile  of  sand, 
fragments  of  brick  or  fibrous  material  in  a  pan  of  oil ;  wire  net 
may  also  be  substituted  for  the  fibrous  or  other  material. 


FIG,  1. 

For  these  burners  to  work  at  all  the  surface,  at  least,,  must  be 
hot,  and  when  acting  in  an  atmosphere  the  latent  heat  of  evapora- 
tion of  the  oil  will  tend  to  keep  the  temperature  downy  resulting 
in  steady  conditions.  There  will  always  be  a  limit  of  rapidity  in 
such  combustion,  since  a  constant  state  will  be  reached  for  the 


FIG 


wick  temperature  and  rate  of  eraporation,  and,  consequently,  for 
the  combustion,  making  regulation  difficult. 

Tr  Such  systems  must  necessarily  be  slow  heat  producers ;  how- 
ever perfect  the  combustion  and  disadvantages  of  the  first  class  of 
gas  combustion,  we  must  add  a  few  more  characteristic  of  the 
methods  of  evaporation. 

Fig,  1  shows  the  simple  pan-wick  system  of  Weeks,  and  Fig.  2 


LIQUID  FUEL  COMBUSTION. 


the  cascade  of  Verstract,  which  is  combined  with  a  wick  at  the 
bottom  to  burn  what  escapes  from  the  cascade.  This  is-  selected 
for  illustration  because  it  is  also  an  example  of  an  attempt  to  pro- 
duce Bunsen  effects  in  the  mixing  of  air  with  the  vapor.  It  does 
not  succeed  in  this,  however,  because  when  the  liquid  surface  is 
present  the  flame  will  locate  there,  and  the  air  blown  through 
the  slits  R  on  the  falling  oil  sheet  can  only  have  the  effect  of  an 
often  renewed  atmosphere,  i.e.,  a  wind ;  no  mixing  of  vapor  and 
air  is  possible. 

8.  However,  the  surface  of  vaporization  is  increased,  hence 
more  vapor  is  produced,  and,  in  addition,  the  air  blown  through 
helps  to  accelerate  the  combustion  ;  but  in  spite  of  this  the  action 
is  precisely  the  same  as  before,  a  flame  of  oil  vapor  burning  in  an 


f 


«*     If     c      \r  Ir 


FIG.  3. 

atmosphere  of  air.     The  improvement  then  is  not  one  of  class  but 
of  detail. 

Improvements  of  the  same  sort  on  the  wick  method,  aiming  to 
lift  the  wick  from  Class  I.  to  Class  II.,  and  get  Bunsen  effects  re- 
sult in  the  same  way.  Air  blown  through  the  wick  chills  it  and 
retards  vaporization,  in  addition  to  slightly  lifting  the  hot  part  of 
the  surface-flame  farther  from  the  vaporization  surface,  which 
should  be  kept  hot.  An  illustration  of  this,  Fig.  3,  is  the  method 
of  Hubbard.  A  mat  is  provided  with  a  pipe  system  to  deliver  oil 
at  numerous  outlets  in  the  mass,  with  the  intention  of  saturating 
the  mass.  Then  air  is  blown  through  the  mat.  The  intention  is 
to  vaporize  the  oil  in  the  mat  by  the  heat  from  above,  and  the 
vapor,  mixing  with  the  air  passing  through,  is  to  ignite  on  the 
top.  It  will  be  readily  seen  that  as  each  outlet  is  a  source  of  oil 
feed  to  the  mat,  we  have  a  large  number  of  wicks  grouped  with 
air  blowing  on  them. 


6  LIQUID   FUEL  COMBUSTION. 

9.  Supposing  a   vaporization    to   take   place   immediately  on 
issuing,  as  is  expected,  and  which  fact,  of  course,  depends  largely 
on  the  fuel  used,  we  will  have  each  nozzle  a  source  of  gas,  and 
there  will  result  a  number  of  gas  jets  blowing  into  the  mat.     The 
ascending  air  current  will  lift  the  gas  jet,  and  there  will  result 
practically  a  cone  of  gas  with  apex  at  the  orifice,    'irrounded  by 
air.     At  the  edges  there  would  be  some  diffusion,  and  beyond  the 
cone  a  moving  atmosphere  of  air.     If  the  mat  were  thick  enough 
and  the  air  current  not  too  swift,  there  might  result  an  approach 
to  a  Bunsen  flame  in  an  atmosphere  of  air  within  the  mat.     If 
the  mat  were  not  thick  enough,  and  the  air  current  moved  too 
fast,  there  would  be  at  the  surface  a  Bunsen  effect.     In  no  case 
could  there  be  an  explosive  effect  of  Class  III.,  because  of  the  rela- 
tion of  air  and  oil  vapor  supply,  the  one  surrounding  the  other, 
making  at  every  point  a  constantly  changing  proportion.     Were 
the  air  and  oil  vapor  discharged  into  the  mat  through  the  same 
orifice   the   effect   would   be    quite   different,  as    will    be    seen 
later. 

10.  Air  blown  on  the  top  of  a  wick  makes  the  flame  a  little 
more  vigorous  only  because  it  renews  the  atmosphere  instead  of 
depending  on  convectk>n,  but  the  process  would  not  change  the 
combustion  otherwise.     The  two  systems  of  surface  evaporation 
from  the  liquid  mass  and  from  the  wick  film  both  demand,  in 
order  that  the  action  may  be  continuous  and  non-clogging,  an 
easily  vaporizable  oil  that  will  not  distil  into  parts  of  different 
vaporization   temperatures.      With   such   an    oil    obtainable,   of 
course  the  next  obvious  step  is  to  simply  boil  it  in  a  retort,  pro- 
ducing vapor  which  can  be  used  exactly  as  gas  and  by  all  the 
means  known  for  gases.     However,  an  additional  precaution  must 
be  taken,  that  of  preventing  decomposition  of  the  vapor  produced 
by  undue  heating  before  burning. 

This  would  be  a  great  advance  over  the  methods  noted  before, 
given  only  the  proper  fuel,  and  we  can  produce  any  sort  of  fire 
from  the  illuminating  flame,  through  Bunsen  and  blow-pipe  effects 
to  the  more  recent  explosive  fires  with  their  high  temperature  and 
rate  of  consumption,  and  with  each  obtain  perfect  regulation. 

11.  To  vaporize  oil  in  retorts  requires  that 

(a)  The  oil  be  not  subject  to  fractional  distillation,  but  that  all 
of   it  must    vaporize   at   the   same  temperature   for  any   given 
pressure. 

(b)  The  temperature  shall  not  rise  above  this  vaporization  tern- 


LIQUID   FUEL  COMBUSTION.  7 

perature  or  decomposition  of  vapor  will  result  with  deposit  of  car- 
bon to  choke  the  passages. 

(G)  The  vapor  once  produced  must  be  prevented  not  only  from 
superheating  before  reaching  the  fire,  but  also  from  condensing. 

These  conditions  are  exceedingly  difficult  to  get,  and  no  oil 
cheap  enough  to  be  used  for  fuel  in  competition  with  coal  is  avail- 
able for  the  system  which  is  otherwise  very  attractive  in  its  sim- 
plicity and  range  of  possible  effects. 

12.  These   oil   vapor   producers  may   be  operated   by  (a)  the 
boiling  of  a  mass  of  oil,  (b)  the  vaporization  of  a  spray,  stream,  or 
drops  by  contact  with  hot  parts,  and  (c)  by  the  carburated  air 
method.     The  first  two,  so  far  as  their  resultant  effects  go  may  be 
grouped  together,  but  the  third  has  been  found  of  value  in  many 
cases  where  the  selection  of  the  required  fuel  is  not  prohibited. 
Air  is  brought  in  contact  with  liquid  surfaces,  and  passing  off 
carries  some  vapor  with  it.     We  have  here  a  mixture  of  air  and 
vapor  burnt  in  the  atmosphere  of  air,  or  we  may  go  farther  and 
form  the  explosive  gas  requiring  no  atmosphere  to  burn.     In  just 
what  proportions  of  air  and  vapor  the  mixture  will  be  delivered 
from  the  carburettor  depends  on  the  temperature  of  the  air,  the 
intimacy  and  length  of  time  of  contact  with  the  liquid,  and  the 
temperature  at  the  evaporation  surface.     Of  course,  the  tempera- 
tures of  the  carburettor  will  tend  through  evaporation  to  become 
continually  lower,  and  this  must  be  guarded  against. 

13.  These  oil  vapor  systems  differ  but  little  from  the  pure  gas 
systems,  and  whatever  can  be  done  with  gas  can  be  done  with 
these  vapors,  giving  fires  of  classes  I.,  II.,  and  III.,  provided  the 
proper  fuel  is  available,  and,  if  the  necessity  for  the  fire  is  so  urgent 
that  cost  is  not  the  most  important  consideration,  they  may  be 
very  useful. 

We  have  not  yet  noted,  however,  any  system  which  will  enable 
us  to  burn  heavy  oils,  or  those  which  fractionally  distil,  leaving  a 
residue  and  of  these  petroleums  and  some  of  the  petroleum 
products  form  the  largest  and  cheapest  source  of  liquid  fuel  sup- 
ply. 

With  the  spray  or  atomizing  system  we  have  something 
radically  different  from  these  so  far  considered,  inasmuch  as  any 
kind  of  oil  may  be  used  and  a  good  fire  obtained  with  each.  Here 
the  oil  passes  through  a  small  opening,  where  it  meets  air  issuing 
at  a  high  velocity  and  is  by  it  thrown  into  the  firebox  as  spray. 
The  firebox  being  filled  with  flame  and  lined  with  brick  also  quiet 


8  LIQUID   FUEL  COMBUSTION. 

hot,  each  particle  of  oil  is  vaporized  in  the  presence  of  air,  and  the 
products  of  combustion  of  previously  consumed  oil  particles. 

14.  The  temperature  of  the  fire  resulting  is  extremely  high, 
and  this  led  to  the  use  of  steam  for  the  spraying  agent,  the 
injecting  nozzle  having  other  openings  through  which  air  passes 
under  the  influence  of  the  chimney  draught  and  partial  vacuum 
produced  by  the  jet. 

The  action  here  is  probably  more  nearly  explosive  than  any- 
thing else.  It  was  noted  that  the  rate  of  propagation  of  com- 
bustion in  explosive  mixtures  is  very  much  increased  by  high 
temperatures.  When  an  explosive  mixture  is  forced  into  an 
enlarged  chamber  previously  made  very  hot,  blow-off  is  prevented 
for  quite  a  range  by  this  increase  in  the  rate  of  propagation.  The 
oils  commonly  used  in  the  spray  have  a  very  high  temperature 
of  vaporization,  and  it  is  more  than  probable  that,  moving  with 
the  air  in  the  hot  parts  of  the  firebox,  at  the  high  temperature 
of  the  mixture  when  vaporization  takes  place,  the  rate  of  prop- 
agation becomes  so  high  that  blow-off  does  not  occur.  How- 
ever the  action  is  not  the  best  even  though  explosive,  for  there 
is  a  large  admixture  of  products  with  the  jet,  particularly  at  the 
edge  and  at  reflecting  surfaces. 

15.  The  entering  jet,  approximately  conical  in  form,   is  com- 
posed of  a  large  number  of  oil  particles,  each  surrounded  by  some 
air  and  some  steam.     As  the  jet  approaches  the  hot  section,  the 
oil  springs  into  gas  and  the  gas  with  the  air  into  flame,  the  steam 
is   inactive   until   very   high   temperatures  are  reached,  when  it 
decomposes  and  acts  as  a  cooler.     The  vaporization  of  the  oil  is 
accomplished  either  in  space  while  the  oil  particle  is  in  motion 
surrounded  by  air,  or  by  contact  with  some  of  the  solid  surfaces 
of   which  a  good   many  are  provided   in   the   form  of  arches, 
bridges,  baffles,  etc.     All  that  can  be  seen  is  an  orange  glow  and 
the  course  of  the  jet  is  invisible,  except  near  the  nozzle. 

The  system  requires  that  the  spray  be  formed,  and  for  this  air 
or  steam  under  sufficient  pressure  must  be  provided,  numbers  of 
baffles  and  bridges  to  break  the  current  after  it  has  entered,  in 
order  to  scatter  the  jet  and  distribute  the  heat ;  a  firebox  of 
sufficient  capacity  to  allow  the  formation  and  vaporization  of 
spray  and  its  final  combustion ;  small  openings  at  the  nozzle. 

16.  Many  auxiliaries  to  the  spray  have  been  used,  but  of  these 
the  most  notable  is  that  of  Kermode,  who  sprays  with  heated  air 
directed  upon  a  bed  of  bricks  or  asbestos  placed  on  the  fire  area. 


LIQUID   FUEL  COMBUSTION.  9 

He  provided  this  loose  fire-bar  covering  simply  to  cover  the  bars 
easily  but  noted  that  by  their  presence  the  action  was  improved, 
for  a  reason  which  will  be  seen  later. 

While  most  of  these  spray  systems  depend  on  a  pressure  drop 
of  air  or  steam  to  atomize  the  oil  and  these  seem  to  have  given 
the  best  satisfaction,  yet  there  are  some  others  which  work  on 
the  few  ounces  pressure  of  a  fan.  The  oil  is  conducted  to  sharp 
points  by  capillary  action  and  blown  from  them  by  the  blast ; 
tests  of  these  generally  show  higher  oil  consumption  than  the 
compressed-air  system,  probably  because  of  the  lower  tempera- 
ture, resulting  from  more  air  and  slower  burning. 

17.  The  subject  of  oil  combustion  in  general  is  very  interesting 
to  the   laboratory  experimenter,  and  as  a  system    was  desired 
which  would  burn  enclosed  under  pressure  for  use  in  the  internal 
combustion-engine,  a  series  of  experiments  was  undertaken  at 
Columbia  University  to  find,  if  possible,  a  method  which  was 
adapted  to  these  conditions. 

With  the  knowledge  of  what  had  been  done  with  oil  fires  in 
other  applications  as  a  guide,  the  first  series  had  for  its  object 
the  determination  of  the  principles  that  should  govern  enclosed 
pressure  fire  systems.  These  principles  once  determined,  it  was 
hoped  that  the  desired  method  would  appear.  Some  of  the 
experiments  made  together  with  the  deductions  therefrom  are 
here  briefly  presented  for  a  record,  as  they  may  be  of  value  to 
other  workers  in  the  field.  Engines  which  work  by  passing  air 
through  a  fire  and  thus  expanding  the  volume  at  constant 
pressure,  impose  on  the  fire  some  conditions  not  easy  to  satisfy. 

18.  Air   must   be   compressed   into   the  firebox,  and   at  each 
delivery  of  the  compressor  there  will  be  a  pressure  increase  on 
the  fire;  similarly  fit  each  admission  to  the  engine  cylinder  there 
will  be  a  pressure  drop,  and  while  we  may  call  the  system  a 
constant  pressure  combustion  system,  this  cannot  be  strictly  true. 
What  is  constant  is  the  mean  pressure,  and  even  this  may  vary 
after  a  limited  time,  for  variation  of  admission  and  cut-off  will 
change  it.     So  that  a  fire  to  work  successfully  in  this  apparatus 
must  be  unaffected  by  pressure  variation  whatever  may  be  its 
extent  or  suddenness. 

One  of  the  greatest  advantages  that  may  be  derived  from  this 

type  of  engine  over  the  explosive,  for  example,  is  the  possibility 

of  employing  the  cheap  and  safe  heavy  oils.     But  to  realize  this 

advantage  we  must  add  to  our  conditions  one  imposing  the  require- 

1* 


10 


LIQUID  FUEL  COMBUSTION. 


ment  that  heavy  oils  shall  be  burnt.  And  finally,  the  products  of 
combustion  must  be  delivered  at  a  constant  temperature,  and  that 
as  high  as  possible.  Moreover,  this  maximum  must  be  known  to 
the  designer  who  proportions  his  cylinders  and  mechanism  for 
some  particular  volume  expansion  dependant  on  this  maximum. 

19.  The  most  radical  difference  between  these  conditions  and 
those  imposed  on  an  ordinary  fire  is  that  of  burning,  enclosed  under 
a  pressure   which   may  vary   widely   and   suddenly ;   so   it   was 
decided  to  first  try  to  obtain  a  fire  which  would  do  this  regardless 
of  the  fuel   used  or  the  delivery  temperature,  and  this  being 
attained  to  experiment   with  the  other  conditions   by  making 
appropriate  modifications. 

20.  One  burner  which  seemed  to  give  a  good  steady  Bunsen 
effect  in   ordinary  use   was  that  of    the  gasolene  or   kerosene 


soldering,  torch,  or  cook  stove.  This  seemed  so  simple  and  un- 
likely to  be  affected  by  pressures  that  the  principle  envolved  was 
that  first  tried,  oil  fed  through  a  self-vaporizing  apparatus  and 
escaping  as  gas. 

Kerosene  was  fed  through  a  coil  of  small  brass  tubing  as  shown 
in  Fig.  4,  the  oil  flowing  from  the  top  toward  the  bottom  burning 
at  B  and  playing  on  the  coil.  It  was  expected  by  a  long  coil  to 
obtain  a  perfect  vaporization.  This  device  was  found  exceedingly 
irregular  in  action,  no  matter  how  carefully  the  feed  was  adjusted, 
the  vapor  delivery  was  never  steady,  varying  from  a  long  flame  to 
total  extinction.  Matters  were  somewhat  improved  by  enclosing 
the  coil  in  a  shell  insuring  a  uniform  heating  throughout.  After 
working  for  some  time  in  this  way  the  operation  stopped,  and 
the  tube  was  found  full  of  solid  carbon  at  the  lower  part,  showing 
a  decomposition  of  vapor  in  that  part.  Gasolene,  alcohol,  etc., 
could  be  used,  but  not  petroleum  and  heavy  oils. 


LIQUID  FUEL  COMBUSTION. 


11 


21.  There  were  two  faults  prominent  in  this  arrangement :  first, 
the  down-feed  through  a  variously  heated  coil,  gave  rise  to  un- 
even vapor  generation ;  second,  the  passage  of  the  formed  vapor 
through  the  heated  part  where  decomposition  could  occur. 

In  the  next  burner  it  was  intended  to  do  away  with  both  of 
these  faults,  the  first  to  be  eliminated  by  having  a  large  mass  of 
liquid  boiling,  and  delivering  vapor  in  such  a  way  as  to  avoid 
superheating  and  so  eliminate  the  second  fault. 

The  apparatus  of  Fig.  5  was  made.  Oil  enters  at  A,  is  dropped 
to  X,  where  it  boils  in  the  chamber,  being  heated  from  below ; 
the  vapor  generated  passes  around  BC,  feeding  the  flame.  B  is  a 
valve  which  permits  shutting  off  vapor  delivery,  and  by  the 
increase  of  pressure  also  the  feed  which  was  under  constant  head. 


FIG.  5. 

Any  rise  of  oil  level  was  prevented  by  the  overflow  D.  Air  enter- 
ing at  the  bottom  with  the  vapor  a  very  good  Bunsen  effect 
could  be  produced  when  burning  free  and  with  naphtha  as  fuel. 
When  enclosed,  however,  and  with  pressure  put  upon  the  chamber 
the  flame  became  very  irregular,  and  any  quick  change  of  pressure 
always  resulted  in  extinction.  With  kerosene  there  was  considera- 
ble vapor  condensation  in  the  drip.  Various  modifications  of 
these  vapor  generating  pressure  oil  burners  were  tried,  but  all  were 
unsatisfactory  for  enclosed  pressure  use.  The  boiling  oil  generates 
within  its  chamber  varying  pressure  depending  on  the  rate  of  boil- 
ing, and  rate  of  efflux  of  the  vapor.  The  rate  of  boiling  or  vapor 
generation,  if  the  flame  below  is  kept  constant,  will  depend  on  the 
pressure  on  the  surface  of  the  liquid. 

22.  This,  in  turn,  depends  upon  the  pressure  on  the  flame  and 
the  size  of  opening  in  the  vapor  pipe.  We  thus  have  a  number 
of  conditions  surrounding  the  vapor  supply,  from  which  the  air 


12  LIQUID  FUEL  COMBUSTION. 

supply  is  free,  but  the  air  supply  has  varying  conditions  of  its 
own,  and  as  these  double  conditions  are  never,  as  it  were,  in  phase, 
the  result  is  failure.  The  only  way  in  which  we  can  keep  the 
proportions  of  air  and  vapor  right  is  by  observing  the  flame,  and 
this  is,  of  course,  out  of  the  question  when  it  is  enclosed.  When 
conditions  can  be  kept  right,  a  very  good  fire  can  be  made  with 
this  burner,  using  kerosene,  gasolene,  naphtha,  alcohol,  etc. 

Some  other  experiments  leading  from  this  brought  out  the  fact 
that  much  better  results  could  be  obtained  if  the  boiling  is  con- 
fined to  the  surface  of  the  liquid  rather  than  allowed  to  exist 
throughout  the  whole  mass.  To  get  this  result  a  pipe  was  bent, 
as  shown,  Fig.  6,  and  oil  fed  from  below  to  the  enclosed  length, 
which  becomes  hot  on  top  from  the  oil  vapor  jet  B.  With  a  con- 
stant head,  a  flame  could  be  kept  lighted  under  pressure,  and 
enclosed  up  to  the  feed-head.  A  sudden  change,  however,  created 


trouble.  The  vapor  delivery  depends  on  the  difference  in  pressure 
between  the  chamber  and  the  feed-head,  and  the  flame  grows 
smaller,  allowing  the  hot  plate  to  cool  when  it  should  be  getting 
hotter.  The  proportions  could  not  be  maintained  at  all  constant 
under  variable  pressure,  though  the  burner  would  work  all  right 
when  proper  adjustments  could  be  made. 

23.  With  a  feed  varying  with  the  chamber  pressure  a  slight 
improvement  resulted,  though  even  then  the  result  was  not  satis- 
factory. There  was  carbonization  at  the  orifice  with  kerosene, 
and  the  apparatus  would  not  work  at  all  with  heavy  oil.  Sudden 
pressure  changes  invariably  caused  extinction.  The  amount 
which  can  be  fed  economically  can  be  varied  but  little,  and  not  so 
to  keep  any  constancy  of  proportions  with  the  air. 

To  maintain  some  such  constancy  of  proportion  was  necessary, 
because  the  ultimate  object  of  the  oil  fire  was  to  heat  the  air,  and 
different  quantities  of  oil  burnt  in  the  same  air  will  give  different 
temperatures  ;  and  if  the  proportion  cannot  be  predicted  certainly 


LIQUID   FUEL  COMBUSTION. 


13 


the  final  temperatures  cannot,  and  the  fire  is  useless  for  the  pur- 
pose in  hand.  With  the  purpose  of  keeping  some  sort  of  ratio 
between  fuel  and  air,  an  air  suction  oil  lift  was  tried,  Fig.  7. 

24.  It  was  not  intended  that  the  complicated  action  of  the  com- 
mon atomizing  spray  should  result,  but  only  that  the  air  should 
lift  oil  in  quantity  somewhat  in  proportion  to  its  own  quantity. 
This  oil  is  blown  with  some  air  through  a  flattened  attenuated 
opening  A,  where  it  is  spread  out  without  changing  its  velocity, 


FIG.  7. 

and  then  brought  in  contact  with  an  externally  heated  plate,  B,  to 
be  vaporized,  the  action  being  similar  in  effect  to  that  of  the 
carburettors  used  in  Priestman  oil  engines.  It  was  found  that 
there  was  one  rate  of  air  feed  at  which  just  the  right  amount  of 
oil  would  lift,  a  variation  either  way  changing  the  action  materi- 
ally. When  enclosed  the  slightest  change  of  pressure  results  in 
bad  action,  sooting,  flooding;  and  extinction.  A  number  of  similar 
injector  oil  lifts  were  made,  and  the  conclusion  reached  was  that 
none  could  be  depended  upon  to  produce  the  action  desired.  To 
further  test  the  principle  of  carrying  oil  by  the  moving  current 


FIG.  8. 

of  air  either  as  mist  or  vapor,  the  arrangement  of  Fig.  8  was  tried. 
Here  an  irregular  mass  of  wire  net  fills  the  chamber  J,  which  is 
about  one-half  full  of  oil.  The  wire  threads  draw  up  by  capillary 
action  the  oil  from  the  surface,  spreading  all  over  the  wires  and 
some  of  the  spaces  between,  making  conditions  very  favorable  for 
the  air  to  take  up  either  mist  or  vapor  as  the  case  may  be.  The 
issuing  jet  is  reflected  back  upon  itself  and  heats  the  nozzle,  insur- 
ing that  any  mist  shall  become  vapor. 


14  LIQUID  FUEL  COMBUSTION. 

25.  The  opening  need  not  be  small.  It  worked  very  well  for  kero- 
sene and  better  for  gasolene,  and  much  better  for  both  when 
heated  air  was  supplied.     This  fact  in  addition  to  that  of  liquid 
collecting  in  the  cone,  J$,  seems  to  indicate  that  a  mist  rather  than 
vapor  was  the  result  of  the  air  passage  over  the  net.     This  fact  is 
further  proved  by  the  working  under  kerosene  without  dropping 
of  temperature  such  as  would  occur  with  evaporation.     With  a 
steady  set  of  conditions  this  apparatus  worked  well  as  was  noted, 
but  like  the  injector  devices,  no  great  variation  of  the  fire  could  be 
made.     It  was  tried  with  petroleum,  and  the  result  showed  a  col- 
lection of  residues  in  A,  only  the  lighter  volatile  parts  coming  off. 
A  little  carbonization  appeared  at  the  nozzle. 

26.  All  these  devices  depending  on  the  vaporization  of  oil  at 
some  point  have  given  great  trouble  from  regulation  when  en- 


FIG.  9. 

closed,  and  none  was  found  satisfactory  for  variation  of  combustion 
pressure.  It  is  probable  that  one  could  be  designed,  but  it  would 
necessarily  be  complicated.  With  the  ones  tried  the  temperature 
of  the  products  could  in  no  way  be  kept  constant,  and  while  most 
required  large  and  variable  excess  of  air,  a  few  were  found  which 
could  be  operated  by  little ;  but  the  high  temperature  resulting 
invariably  produced  vapor  decomposition.  They  required,  more- 
over, special  oils,  but  even  this  might  be  endured  if  a  steady 
fire  with  always  the  same  temperature  delivery  could  be  made  to 
work  under  variable  pressures ;  but  these  results  could  not  be 
obtained. 

27.  The  vaporization  systems  were  now  abandoned  in  view  of 
these  difficulties   for  the  attractive  simplicity  of  wick  combina. 
tions  which,  while  perhaps  not  offering  the  greatest  perfection  of 
combustion,  yet   would   not   go  out  when  put   under   pressure, 
Fig.  9  was  tried,  with  a  bottom  oil  feed  to  the  wick,  and  air  sup- 


LIQUID   FUEL  COMBUSTION.  15 

plied  above.  It  was  found  that  the  wick  at  the  bottom  of  the 
chamber  was  not  affected  by  pressure,  and  burned  steadily  when 
enclosed,  but  a  steady  discharge  was  necessary,  for  when  the  dis- 
charge was  interrupted  the  flame  was  extinguished.  It  seems  as  if 
the  products  must  be  conducted  away  at  once,  and  this  is  probably 
because,  with  the  wick,  the  vapor  generation  will  go  on  some  time 
after  the  oxygen  supply  fails.  It  also  seemed  advisable  to  have 
the  air  current  and  flame  tend  towards  the  same  opening  and  not 
oppose.  Opposition  produces  a  violent  flame  and  irregular  action 
which  may  cease  entirely  at  any  time. 

28.  To  improve  the  means  of  renewing  the  atmosphere  of  this 
fire  the  burner  of  Fig.  10  was  made.  A  is  an  asbestos  mat  sup- 
plied with  oil  from  B.  C  is  the  air-supply  pipe  ending  in  the 
funnel  Z>.  If  the  oil  be  lighted  at  A,  and  time  allowed  for  the 
whole  to  heat  up,  the  burner  can  be  enclosed  and  pressure  applied 


FIG.  10. 

through  the  air-supply  C  without  causing  extinction.  The  pres- 
sure in  the  combustion-chamber  has  absolutely  no  effect  on  oil 
flame  thus  produced. 

29.  The  products  of  combustion  thus  produced  were  piped  to 
a  small  Shipman  steam-engine  to  observe  the  effect  of  the  impulse 
of  engine  admission  on  the  action  of  the  fire.  Good  results  for 
any  pressure  were  obtained  with  only  one  drawback.  If  the  velo- 
city of  the  air  over  the  flame  be  too  high,  the  flame  will  go  out. 
With  gas  or  oil  previously  vaporized  a  surplus  as  well  as  a  deficiency 
of  air  will  cause  extinction  ;  here,  any  surplus  will  have  no  effect, 
provided  only  that  it  move  slowly  enough.  A  most  important 
result  was  here  attained,  viz.,  the  flame  could  be  kept  going  under 
working  conditions. 

For  a  more  perfect  and  rapid  combustion  of  oil  by  the  wick 
method,  it  seemed  desirable  to  keep  the  flame  hot  even  beyond  its 
visible  part,  and  everywhere  supplied  with  fresh  air.  This  could 
be  done  either  by  drawing  the  flame  out  to  a  thin  sheet,  or  by 
shooting  across  it  warm  air  currents,  as  in  the  blow-pipe.  Ac- 


16 


LIQUID  FUEL   COMBUSTION. 


cordingly,  the  apparatus  of  Figs.  11  and  12  were  constructed. 
In  A  is  asbestos,  on  top  of  which  the  oil  rests,  and  through  which 
oil  trickles  to  the  part  below  enclosed  between  pipe,  (7,  and  sur- 
rounding pipe,  B.  The  flame  having  been  started  at  /,  air  was 
turned  on  through  (7;  the  flame  was  conical,  with  a  well  defined 


FIG.  11. 

blue  interior,  and  was  blue  even  at  the  tip.  This  method  of  feed 
might  be  duplicated  by  dropping  oil  In  varying  quantities  on 
the  loosely-packed  wick  if  a  variable  combustion  is  desired.  This 
burner  can  be  enclosed  and  put  under  pressure,  and,  moreover,  un- 
like the  last,  is  not  sensitive  to  change  of  velocity  of  air  through 
it. 
30.  While  not  all  the  conditions  desired  are  here  met,  many 


FIG.  12. 

that  are  most  important  are  fulfilled.  The  burner  will  work,  en- 
closed, fairly  steadily,  and  is  not  affected  by  pressure  changes,  but 
it  always  requires  a  large  excess  of  air,  and,  therefore,  delivers 
products  whose  temperature,  though  fairly  constant,  is  yet  not  the 
maximum.  Fig.  12  was  made  to  be  an  advance  on  this  type,  by 
introducing  a  hot  air  blow-pipe  effect.  The  flame  here,  instead  of 


LIQUID   FUEL   COMBUSTION.  17 

having  a  blue  center,  has  a  deep  yellow  core  forced  by  the  air 
currents  into  blue  at  the  edges.  The  center  is  the  gas  generator, 
which  gas  is  completely  burned  at  the  edges  by  air  from  the 
heated  lips  of  the  tangent  tubes.  External  heating  to  redness 
will  cause  internal  ignition,  and  wicks  placed  in  the  path  of  the 
products  seem  to  improve  the  action,  both  in  completeness  of  com- 
bustion and  as  re-lighting  after  extinction.  This  burner  could  be 
used  with  satisfaction  in  every  point,  except  that  it  used  such 
large  quantities  of  air  and  delivered  products  of  comparatively 
low  temperature. 

31.  The   tendency   of   the  preceding   experiments  is  evident, 
always  away  from  special  vaporizers  to  arrangements  with  autom- 
atic regulation,  the  vaporization  taking  place  in  the  firebox,  in  the 
presence  of  air  if  possible,  and  so  preventing  not  only  decomposi- 
tion and  carbonization,  but  also  condensation.     It  seems  rather 
odd  that  in  general  the  means  which  worked  best  under  the  diffi- 
cult conditions  imposed  were  in  general  the  simplest.     For  the 
use  of  all  oils,  including  those  of  low  and  those  of  high  boiling 
points,  probably  the  following  conditions  would,  'if  they  could  be 
fulfilled,  produce  a  very  good  oil  fire  : 

The  oil  to  be  introduced  as  liquid  with  the  air  and  brought  im- 
mediately, still  with  the  air,  to  the  hottest  part  of  the  fire,  with 
means  added  to  prevent  the  mixture  of  the  vapor  thus  produced 
and  its  air  from  mixing  with  products  of  combustion  of  matter 
already  burnt.  At  the  time  these  conditions  were  formulated,  it 
seemed  impossible  that  any  apparatus  could  be  constructed  which 
would  permit  of  such  action ;  but  in  fact,  such  an  apparatus  was 
found,  and  worked  so  well  as  to  entirely  justify  all  the  labor  of 
classification  and  minute  experimental  observation,  which  made  it 
possible  to  predict  what  conditions  should  produce  a  good  method, 
even  when  the  means  seemed  impossible  to  find. 

32.  This  resultant  method  was  not  the  outcome  of  this  series  of 
experiments  alone,  but  rather  of  the  combined  oil  and  gas  exper- 
iments, some  of  which  have  been  previously  reported.     Just  about 
the  time  the  experiments  above  described  were  completed,  and  the 
probably  necessary  conditions  for  the  good  oil  fire  formulated,  the 
explosive  gas-fire  described  in   the   author's  paper,  No.  923,  Vol. 
XXIII.,  p.  292,  was  discovered. 

By  the  use  of  the  explosive  mixture,  a  fire  can  be  made  in  a 
closed  chamber,  requiring  no  atmosphere  beyond  the  mixture  fed, 
and  such  a  fire  will  deliver  hot  gasses  at  a  constant  unvarying 


18 


LIQUID   FUEL  COMBUSTION. 


temperature,  no  matter  what  the  quantity  burned ;  this  tem- 
perature is  the  maximum  possible,  as  no  excess  of  air  is  heated  ; 
and,  finally,  this  very  excellent  fire  calls  for  no  special  apparatus, 
requiring  simply  an  opening  through  which  the  feed  must  be 
made  at  a  rate  exceeding  the  rate  of  propagation,  which  opening 
is  surrounded  by  a  pile  of  broken  rock.  The  function  of  this 
broken  rock  is  to  decrease  the  velocity  of  translation  by  increasing 
the  area  of  cross-section  of  the  advancing  stream,  and  to  increase 
the  rate  of  propagation  of  inflammation  by  heating  until  these 


FIG.  13. 

two  rates   become  equal,  allowing  the  combustion    to  localize 
within  the  fragments. 

33.  This  suggested  a  revival  of  the  experiments  on  oil  along  the 
lines  laid  down  as  follows  :  It  was  desired  to  vaporize  the  oil  and 
produce  with  the  vapor  an  explosive  mixture  which,  in  return, 
was  to  burn  under  pressure  as  desired  in  one  of  the  explosive 
burners.      The  apparatus  in  Fig.  13  was  constructed  to  do  this ; 
gasolene  is  held  in  a  chamber  kept  at  about  60  degrees  Fahr.,  and 
bubbles  through  from  A,  the  carburetted  air  was  rendered  ex- 
plosive by  the  manipulation  of  the  by-pass  B,  admitting  pure  air 
above  the  liquid.     The  resulting  explosive  mixture  was  burnt  in 
the  explosive-burner,  C. 

34.  This  arrangement  fulfilled  the  requirements  exactly  so  far 
as  this  particular  fuel  was  concerned,  giving  a  fire  under  pressure 


LIQUID   FUEL  COMBUSTION. 


19 


not  affected  by  any  changes  in  pressure  however  sudden,  and 
delivering  at  all  feeds  hot  products  of  exactly  the  same  tem- 
perature. 

This  burner  was  also  piped  to  the  steam-engine  and  a  second 
by-pass,  />,  permitted,  keeping  the  temperature  of  the  air  entering 
the  engine  under  perfect  control.  Wide  variations  of  speed  and 
pressure  had  no  effect,  neither  had  the  pulsation  due  to  engine 
admission  and  cut-off. 

35.  Here,  then,  was  a  very  encouraging  result,  but,  unfortun- 


FIG.  14. 

ately,  only,  the  fuels  easily  vaporized,  such  as  naphtha,  gasolene, 
benzine,  alcohol,  etc.,  were  available. 

The  next  step  was  an  attempt  to  utilize  kerosene  in  a  somewhat 
similar  way.  To  this  end  the  apparatus  of  Fig.  14  was  set  up. 
Here  oil  is  fed  to  chamber  A  and  kept  at  variable  level ;  air  is 
admitted  at  B  and  passing  C  throws  a  spray  into  D  where  it  is 
vaporized  by  the  heat  of  the  fire ;  the  end  D  being  covered  with 
the  rock  an  explosive  fire  resulted,  the  correct  proportion  of  air 
to  vapor  being  maintained  by  varying  the  air  supply  and  oil  fuel. 

Thus,  while  it  worked  under  some  circumstances  and  gave  a 
very  satisfactory  fire,  showed  the  same  trouble  that  was  experi- 
enced with  sprays  in  the  other  series  of  experiments  and  was 


20  LIQUID   FUEL  COMBUSTION. 

abandoned  for  the  device  there  found  to  be  more  satisfactory, 
i.  e.,  a  surface  boiling  of  the  liquid.  Fig.  15  shows  the  device 
constructed  for  this  purpose. 

36.  Air  was  admitted  at  A,  and  with  it,  at  first,  some  gas,  mak- 
ing an  explosive  fire  at  B.  The  oil  was  fed  from  below  to  the 
cone  under  the  plate,  -C,  heated  from  above,  Yarying  level 


exposed  more  or  less  surface  to  be  heated  and  varied  the  distance 
from  the  fire  plate.  The  regulation  in  practice  was  not  as  good 
as  one  might  expect  from  the  device.  The  vaporization  by 
approach  of  the  oil  to  the  hot  parts  suggested  the  next  step 
which  is  so  obvious  that  it  seems  as  if  it  should  have  been  tried 
first.  This  was  to  simply  feed  the  oil  and  air  through  the  same 
pipe  to  a  pile  of  rock  where  the  explosive  fire  is  maintained,  with 
the  expectation  that  the  hot  pipe  will  do  the  vaporizing.  The 
oil  is  fed  through  cock  A,  Fig.  10,  and  the  air  through  B,  both 
reach  the  fire  through  the  same  pipe  (?,  and  burn  explosively  in  the 


FIG.  16. 

mass  of  rock.      This  was  eminently  satisfactory,  and  showed  an 
action  which  was  very  fine,  if  unexpected. 

37.  When  the  feed  is  slow  the  pipe  C  becomes  hot  and  then 
does  undoubtedly  act  as  a  vaporizer,  but  when  the  feeds  are  in- 
creased the  fire  is  forced  away  from  the  nozzle,  as  in  the  case  of 
gases,  and  the  pipe  C  remains  almost  cold,  no  matter  how  hot  the 
fire  in  the  rocks,  but  the  perfection  of  the  action  is  maintained 


LIQUID   FUEL  COMBUSTION.  21 

and  it  is  found  that  not  the  pipe,  C,  but  the  hot  rocks  themselves 
act  as  the  vaporizer.  The  air  and  oil  impinge  together  on  the 
hot  mass,  spreading  out  in  constant  velocity  surfaces;  the  com- 
bustion takes  place  on  that  surface  where  the  velocity  is  equal 
to  the  rate  of  propagation  and  in  the  passage  the  oil  automati- 
cally vaporizes  by  contact  with  the  same  rocks  which  make  the 
explosive  fire  possible,  and  all  this  happens  without  diffusion  with 
the  products  of  previous  combustion.  Thus  the  function  of  the 
rocks  becomes  complicated ;  first,  starting  with  gas  the  explosive 
fire  is  made  possible  by  their  presence,  and  the  result  is  the  heat- 
ing of  the  entire  mass  from  top  to  bottom,  the  mass  thus  heated 
is  a  perfect  vaporizer  for  the  oil,  which,  fed  with  its  air  makes  an 
explosive  mixture  and  maintains  the  temperature  of  the  rocks, 
the  whole  interrelated  series  of  actions  and  reactions  producing 
what  I  have  named  the  "  Explosive  Oil  Fire." 

38.  Were  the  proportions  not  explosive  the  interior  of  the  mass 
would  chill  and  the  vaporization  would  stop.     It  is  a  very  strik- 
ing experiment  to  withdraw  the  nozzle  from  the  intensely  glowing 
mass  of  rock,  of  a  properly  working  fire,  and  note  the  oil  drip, 
drop  by  drop,  giving  off  each  time  a  dull  red  flash  and  a  cloud  of 
smoke,  while  the  whole  rock  mass  cools  down ;  a  re-insertion  of 
the  nozzle  causes  at  once  a  resumption  of  the  intense  rapid  high 
temperature  combustion.     And,  secondly,  by  a  simple  change  of 
proportion  observe  an  instant  cessation  of  the  action,  producing 
first  smoke  and  then  total  extinction. 

This  method  of  burning  the  oil  is  perfectly  adapted  to  the  pur- 
pose for  which  it  is  designed,  i.e.,  the  combustion  of  any  oil  in  a 
closed  pressure-chamber,  as  already  described,  and  the  action 
leaves  nothing  to  be  desired. 

39.  Naturally   the  next   question   would  be  to  determine  the 
action  with  residue  oils  of  petroleum.     It  need  only  be  remarked 
here  that  with  every  oil  tried  the  action  was  the  same ;  and  three 
fires  side  by  side,  burning  respectively  kerosene,  cylinder  oil,  and 
linseed  oil,  showed  no  difference  in  action.     The  so-called  residue 
oils  leaves  no  residue  this  way.     The  experiment  of  feeding  the 
several  oils  successively  through  the  same  fire  without  interrup- 
tion resulted  in  no  apparent  change  of  action.     We  can  now  see 
how  the  action  of  the  brick  that  Kermide  placed  on  his  grates 
improved  the  action,  which  would  have  been  still  further  im- 
proved if  the  spray  had  been  prevented  from  diffusing  with  pro- 
ducts before  reaching  the  brick.     Moreover,  by  this  simple  change 


22  LIQUID   FUEL   COMBUSTION. 

the  spraying  process  would  be  rendered  unnecessary.  Also  in  the 
case  of  the  saturated  mat  referred  to  in  the  earlier  part  of  the 
paper,  it  will  now  be  readily  seen  how  the  feeding  of  both  oil  and 
air  through  the  same  opening,  instead  of  as  designed,  would  have 
completely  changed  the  action. 

Originally  firebrick  fragments  were  used,  but  the  fire  was  in- 
tensely hot,  and  fused  such  fragments  together,  even  fluxing 
them  and  causing  a  flow.  Later  other  rocks  were  tried,  and  mag- 
nesite  was  found  not  to  fuse ;  dolomite,  also  infusible,  crumbles 
slightly. 

It  was  noted  in  the  experiments  on  gas  that  considerable  gas 
might  be  added  to  a  mixture  in  excess  of  that  required  for 
chemical  proportions  without  injuring  the  explosive  properties  of 
the  resulting  mixture,  which  fact  was  of  value  in  producing  sur- 
face flames  above  the  explosive  fires  ;  of  course,  there  will  be  a 
point  where  the  explosive  property  will  be  lost  and  extinction 
ensue. 

40.  When  an  excess  of  oil  was  tried  the  explosive  fire  between 
the  rock  fragments,  which  act   as  the   automatic   non-diffusing 
vaporizer,  was  maintained  by  the  lower  and  explosive  part  of  the 
fire,  while  the  excess  of  oil  passed  on  to  be  burned  above.     It 
was  found  possible  to  varf  the  oil  100  per  cent,  without  stopping 
the  explosive  action  below,  the  effect  being  merely  a  variation  in 
the  length  of   the  surface  flame.     This  variation  at  will  in  the 
character  of  the  surface  flame  is  of  no  importance  in  the  problem 
which  was  originally  set,  i.e.,  the  production  of  a  fire  for  an  in- 
ternal combustion  engine  working  by  the  increase  of  volume  at 
constant  pressure.     It  is,  however,  of  the  utmost  importance  in 
metallurgical  and  steam-boiler  furnaces,  and  a  few  experiments 
other   than   those   originally   set   were   made   on    these  applica- 
tions. 

41.  Fig.  17  shows  a  series  of  burners  which  were  used  experi- 
mentally with  success  on  both  open  and  closed  fires,  showing  the 
great  simplicity  that  here  meets  with  success.     The  one  at  the 
lower   left-hand  corner,  shows  an  air  chamber    of    2-inch    pipe 
through  which  the  oil  pipe  is  led,  the  air  and  oil  passing  down- 
ward at  an  incline  of  about  30  degrees  to  the  rock  bed.     Propor- 
tions of  mixture  are  maintained  by  external  valves ;  the  outlets 
may  in  this  type  be  easily  duplicated. 

The  one  passing  the  stool  shows  a  down  bending  quarter  pipe 
fed  with  air  and  oil,  and  provided  with  a  starting  gas  cock.  About 


LIQUID   FUEL   COMBUSTION. 


23 


one  square  foot  of  rock  several  inches  thick  can  be  kept  in  a  glow 
with  this. 

42.  To  show  that  the  theory  of  the  formation  of  combustion  sur- 
faces holds  with  this  oil  tire  as  with  the  gas,  a  pile  of  broken  brick 
was  arranged  to  run  about  fifteen  minutes,  covered  with  clay ;  the 
result  is  shown  on  the  top  of  the  chair,  a  round  cavity  was  fused 
out  and  a  center  lump  left,  showing  what  would  be  expected  with 


FIG.  17. 


this  down  bending  nozzle  from  the  theory,  viz.,  an  annulas  form 
of  combustion  surface. 

The  plate  on  the  floor  at  the  right  is  tapped  to  receive  from  be- 
low the  nozzle  lying  on  the  top  containing  a  center  vertical  oil 
feed  surrounded  by  the  air  feed.  This  does  not  work  well  on  a 
flat  plate  as  some  oil  collects  in  a  circle  on  the  plate,  where  it  meets 
little  air,  and  is  moreover  chilled  by  the  plate,  a  conical  brick 
bottom  works  better. 


LIQUID   FUEL  COMBUSTION. 


Two  6-inch  nipples  arranged  for  closed  fire-pots  are  shown, 
the  lower  one  provided  with  oil,  air,  and  gas  inlets  delivering  to 
a  pipe  which  merely  enters  the  wall  of  the  fire  chamber.  This 
works  very  well;  after  heating  by  a  properly  proportioned  mix- 
ture, the  whole  becomes  dazzingly  hot,  and  a  blue  to  orange  surface 


FIG.  18. 

flame  several  feet  high  can  be  obtained  without  disturbing  the  ac- 
tion of  the  lower  fire.  While  the  whole  firepot  is  white  hot  and 
would  melt  in  time,  the  horizontal  feed  pipe  is  always  cool  enough 
to  be  borne  by  the  hand.  The  very  high  temperatures  that  can  be 
produced  may  be  easily  estimated  when  it  is  stated  that  this 
burner  can  consume  a  gallon  of  crude  petroleum  in  about  ten  min- 
utes, and  in  so  doing  uses  no  excess  of  air. 


LIQUID   FUEL  COMBUSTION. 

43.  The  upper  nipple  shown  is  connected  for  use  with  gas,  and 
is  provided  with  a    1-inch  clay  lining.      It  is  fed  from  below 
with  a  mixture  of   air  and  gas  from    the   motor-driven   6-inch 
positive  blower.     This  was   used   for  melting  crucibles  of  tin, 
aluminum,  lead,  copper,  etc.,  in  the  calibration  of  a  Le  Chatelier 
pyrometer  for  some  experimental  determinations  of  the  passage  of 
heat  through  metal  from  a  hot  gas  to  a  cold. 

44.  In  the  center  of  the  shelf  is  shown  a  2£-inch  cross  bottom 
fed  by  air  and  gas  direct  from  the  mains  and  used  for  heating 
soldering  irons.     Kerosene  has  also  been  used  in  this  apparatus  for 
the  same  purpose. 

The  first  application  of  this  method  of  combustion  to  a  steam 
boiler  is  illustrated  in  Fig.  18.  The  oil  tank  in  the  rear  has  a 
delivery  pipe  starting  at  the  bottom  of  the  tank,  and  air  from  the 


FIG. 


main  is  piped  to  the  oil  surface  and  to  the  burner  through  the 
hose  ;  a  slight  throttling  at  the  boiler  will  put  enough  pressure  in 
the  oil  to  lift  it  to  the  burner,  where  it  passes  the  valve  seen  in  the 
right  front.  A  half-inch  pipe  leads  to  the  center  of  the  firebox 
and  then  turns  down  by  an  elbow  ;  the  grate  is  covered  with  clay 
and  the  firepot  filled  with  broken  rock  A  gas  connection  is 
shown  for  initial  heating  and  a  steam  pipe  passes  from  the  dome 
vertically  downward  in  front.  It  was  for  observing  the  action  of 
steam  in  the  fire  that  this  particular  apparatus  was^set  up.  It  was 
hoped  that  by  the  decomposition  of  the  steam  in  the  fire  the 
excessively  high  temperatures  would  be  avoided  and  the  use  of 
special  rock  of  high  fusing  point  rendered  unnecessary.  If  the 
fire  be  started  and  brought  to  a  steady  glow  and  steam  be  then 
admitted,  there  will  at  once  appear  an  almost  invisible  surface 
flame  showing  the  action  desired,  a  decomposition  of  steam  in  the 
hottest  parts  and  a  recombination,  more  or  less  complete,  beyond 
at  the  surface.  The  steam  is  thus  a  sort  of  heat  distributor,  and 


26  LIQUID   FUEL  COMBUSTION. 

in  this^way  it  was  found  feasible  to  use  common  fire-brick;  an 
occasional  sticking  together  is  easily  broken  up  at  the  end  of  a  run 
by  a  bar,  and  everything  made  as-  good  as  new. 

45.  It  was  also  thought  worth  while  to  try  what  could  be  done  in 
producing  reverberatory  action,  similar  to  that  of  coal  fires.     To 
this   end,  this   apparatus,  Fig.  19,  was  made  of   brick  and  clay. 
With  a  5-inch  fire  at  A,  and  an  air  inlet  at  B  and  (7,  a  good  hot- 
colorless  flame  2  feet  long  could  be  produced,  heating  the  chamber 
D  to  an  even  glow  with  an  atmosphere  reducing  or  oxdyzing  as 
desired. 

It  should  be  noted  that  all  of  the  explosive  burners  described 
will  work  under  any  air  pressure  whatever,  a  variation  merely 
altering  the  distance  of  the  combustion  surface  from  the  outlet, 
but  for  burning  a  given  amount  of  oil  a  larger  air  pipe  must  be 
used  with  low  pressure  air  feeds  than  with  high. 

46.  In  conclusion,  it  may  be  said  of  the  method  resulting  from 
this  experimental  research  that   it   seems   to  be   in   every   way 
satisfactory  for  the  purpose  for  which  it  was  derived,  and  may  be 
of  use  in  other  applications.     It  has  no  small  openings  for  oil,  no 
possibility  of  carbonizing;  will  burn  any  oil  with  air  at  any  pressure, 
provided  only  that  enough  air  be  supplied,  and  is  subject  to  an 
almost  unlimited  variation  of  form ;  it  will  deliver  gases  at  a  con- 
stant and  maximum  temperature,  which  may  be  lowered  to  any- 
thing desired  by  air  dilution  ;  is  capable  of  burning  more  oil  in  less 
volume  than  any  of  the  other  forms  tried,  and  this  with  the  least 
possible  amount  of  air.     It  must  be  stated  as  a  drawback  that 
without  the  use  of  steam  it  calls  for  the  use  of  selected  rock  to 
prevent  fusion. 


PHYSICAL  PROPERTIES  OF  EXPLOSIVE  MIXTURES. 

Power  generation,  involving  as  one  of  its  phases  the  internal 
combustion  method  of  heating  a  gas,  demands  a  knowledge  of  the 
properties  of  explosive  mixtures  not  only  qualitatively,  but  quanti- 
tatively as  well.  For,  internal  combustion  presupposes  the  fuel 
and  requisite  air  in  proper  or  otherwise  known  proportionate 
amount  introduced  into  the  closed  system,  and  investigation  has 
shown  that  to  obtain  the  best  results  in  heated  products  of  combus- 
tion these  two  elements — the  fuel  and  air — should  be  mixed  before 
combustion,  producing  thereby  an  explosive  mixture.  Moreover, 
it  has  developed  that,  no  matter  whether  the  fuel  be  liquid  or  gas, 
the  explosive  combustion  of  the  resulting  explosive  mixture  is  not 
only  the  best  from  the  point  of  view  of  physics,  but  also  from  that 
of  simplicity  and  practicability,  that  is,  it  is  not  only  the  best 
way,  but  it  is  the  simplest  and  easiest  to  carry  out. 

Researches  by  very  eminent  scientists  on  this  subject  have 
shown  :  ( i )  That  explosive  mixtures  have  properties  not  possessed 
by  other  mixtures,  (2)  they  have  pretty  well  developed  the  nature 
of  these  special  qualitative  properties  and  (3)  they  have  measured 
the  extent  and  intensity  of  many  of  these  physical  reactions  of  these 
mixture.  But  in  spite  of  the  information  developed  by  these  men 
the  fact  remains  that  to-day,  when  we  are  so  extensively  using 
explosive  mixtures  in  our  exploding  gas-engines  and  contemplating 
their  utilization  in  other  ways,  there  does  not  exist  data  sufficient 
for  the  calculations  of  many  of  the  quantities  needed,  nor  is  there 
obtainable  apparatus  sufficiently  reliable  and  practicable  to  enable 
designing  engineers  to  obtain  the  data  needed  for  their  work.  It 
has  been  the  aim,  then,  of  this  part  of  the  work  not  only  to  work 
out  if  possible  a  properly  simple  and  accurate  means  for  obtaining 
such  data,  but  also  to  use  the  apparatus  in  the  making  of  such 
observations  as  time  might  permit.  Before  entering  into  the  work 
forming  the  subject  matter  of  this  chapter  it  seems  advisable  to 
first  look  at  the  work  of  the  scientists  referred  to  and  to  note  their 
results. 

Bunsen,  in  the  course  of  his  work  on  gas  analysis  considered: 


2  THE  HEAT  ENGINE  PROBLEM. 

(i)  The  heat  of  combustion  of  a  gas;  (2)  the  temperature  of 
combustion;  (3)  "  the  explosive  force  of  gases  ";  (4)  temperature 
of  ignition  of  gases,  and  (5)  limit  of  inflammability  of  mixtures, 
as  influenced  by  dilution.  All  of  these  were  undertaken  chiefly 
in  reference  to  one  phase  of  his  system  of  analysis,  i.  e.}  the  deter- 
mination of  combustible  gases  in  a  heterogeneous  mixture  under 
analysis. 

The  heat  of  combustion  he  calculates  from  that  of  elements 
determined  by  analysis,  using  the  elemental  values  of  Favre  and 
Silberman.  The  temperature  of  combustion  and  "  explosive 
force,"  or  pressure  after  constant  volume  combustion,  are  calcu- 
lated from  this  last  by  assumption  of  a  constant  value  of  Cv. 
Under  temperature  of  ignition  he  simply  noted  that  a  gas  which, 
by  reason  of  dilution,  became  uninflammable  regains  its  combusti- 
bility if  prevented  from  expanding  freely  during  ignition  or  when 
its  temperature  is  raised.  Under  limit  of  inflammability  it  was 
observed  that  inflammable  mixtures  might  be  rendered  uninflam- 
mable by  dilution,  and  that  the  point  of  difference  is  sharply 
marked.  His  table  is  : 

i  Volume  of  detonating  gas  with{|;|  CO.  is 

i  Volume  of  detonating  gas  with^  H  i. 


He  also  determined  some  rates  of  propagation  of  explosive 
mixtures  with  the  pressure  tank  and  orifice  method  ;  results  later 
shown  to  be  quite  erroneous. 

Following  him,  whatever  was  done  by  other  individual  investi- 
gation was  overshadowed  by  the  work  of  Berthelot  and  Vielle 
ariti  Mallard  and  Le  Chatelier.  The  only  extensive  work  under- 
taken with  the  sole  object  of  studying  the  properties  of  explosive 
mixtures  was  that  of  Mallard  and  Le  Chatelier,  published  in  var- 
ious papers,  and  collected  and  republished  in  the  collected  works 
of  the  "  Commission  de  Orison,"  1883,  with  the  title  "  Recherches 
Experimentales  et  Theoretiques  sur  la  Combustion  des  Melanges 
Gazeux  Explosifs  par  MM.  Mallard  et  Le  Chatelier  Ingenieurs 
au  Corps  des  Mines." 

They  say  in  the  introduction  :  "  We  have  not  limited  our  work 
to  mixtures  formed  by  air  and  fire  damp  ;  we  have  extended  it  to 


CYCLIC   ANALYSIS   OF    HEAT   ENGINES.  3 

the  principal  combustible  mixtures.  We  believed  that  we  should 
thus  be  able  to  profit  by  apparatus  often  costly,  set  up  by  us, 
and  by  the  experience  gained  in  its  manipulation  to  furnish  to 
science  some  new  facts  on  questions  still  but  little  known  "  (1883). 

This  work  and  notes  on  that  of  previous  investigations,  which 
is  reported  in  some  three  hundred  pages  and  several  plates  of  cuts, 
was  divided  into  three  parts  : 

i.  Conditions  necessary  for  starting  active  combustion  and  the 
temperature  of  inflammation. 

2.  The  rate  with  which  inflammation,  once  started,  will  propa- 
gate itself  through  the  gaseous  mass,  and  in  general  the  circum- 
stances characterizing  that  propagation. 

3.  The  pressure  produced  in  a  closed  vessel  after  the  combus- 
tion of  the  gaseous  mixture  enclosed  in  it,  from  which  can  be 
deduced:  (a)  Law  of  cooling  of  hot  gases  in  cool  walls  (b) 
temperature  produced  by  combustion;  (c)  nature  of  variation  of 
specific  heat  at  high  temperature. 

The  subject  of  temperature  of  inflammation  is  treated  as 
follows : 

Historical. — The  work  of  Davy,  who  observed  that,  at  times, 
when  a  metal  bar  while  hot  might  not  inflame  mixture  a  flame  will. 
He  arranged  some  gases  in  order  of  inflammability :  Marsh  gas, 
ethylene,  carbonic  oxide,  hydrogen  and  phosphoretted  hydrogen. 
To  the  last,  PhH3,  he  gave  116°  C. 

Davy  also  noted  that  slow  combustion  unaccompanied  by  heat 
and  light  always  took  place  in  mixtures. 

After  him,  Bunsen,  who  worked  on  questionable  theoretic 
grounds,  gave  these  figures : 

i  Volume  (H  +  O)  +  2.85    Volumes   of   CO2 1790°  C. 

+  3-65   Volumes    "    H 2116°  C. 

+     10   Volumes     "     0 857°  C. 

Nothing  more  was  found,  probably  due  to  difficulties. 

Method  of  Experimenting. — After  considering  several  methods 
all  are  rejected  as  inaccurate  or  impracticable  except  the  one 
adopted.  Mixture  is  admitted  rapidly  into  a  chamber — previously 
heated  to  a  known  temperature — which  may  be  empty  or  filled. 
Both  methods  were  used.  It  is  then  observed  whether  the  gas 
ignites  or  not,  and  two  limiting  temperatures  can  be  determined 


4  THE  HEAT  ENGINE  PROBLEM. 

between  which  the  temperature  of  ignition  must  lie.  It  was 
found  very  slow  work  and  difficult  to  avoid  both  accidental 
and  systematic  errors;  however,  results  were  tabulated  for  mix- 
tures of  H  and  air  in  all  proportions  and  diluted  with  CO2  and  O. 
Similarly  for  CO  and  C2H4,  fire  damp.  The  limits  in  the  three 
cases  are  for  all  mixtures : 

H>  5I7-5950,  mixed   with  air,   O  and   CO,. 

CO,          630-725°,  mixed  with  air,   O  and  CO2. 
CHj,       640-760°,    mixed  with  air  and  O. 

Experiments  on  slow  combustion  show  a  discontinuity  between 
it  and  that  accompanied  by  light  and  heat  changes. 
The  whole  is  summarized  as  follows  : 
The  temperature  of  inflammation  can  be  fixed  at 

555°   for  explosive  mixtures  of   H  and  O. 
655°     "  "    CO  and  O. 

656°     "  "    GH4  and  O. 

The  addition  to  explosive  gas  of  even  a  considerable  volume  of 
inert  gas  modifies  little  or  not  at  all  the  temperature  of  inflam- 
mation. 

However,  with  mixtures  of  CO  and  O  the  addition  of  notable 
quantity  of  CO2  seems  to  elevate  that  temperature  to  a  sensible 
degree.  One  volume  of  CO2  added  to  explosive  mixtures  CO  +  O 
raises  the  temperature  from  655°  to  700°. 

For  mixtures  in  which  H  and  O  are  the  elements  the  com- 
bustion takes  place  as  soon  as  the  temperature  of  inflammation  is 
reached.  It  is  entirely  otherwise  for  marsh  gas,  which  we  may 
liken  to  fire  damp.  The  mixtures  formed  by  this  gas  with  air  or 
oxygen  do  not  burn  except  after  having  been  brought  to  and  kept 
ten  seconds  perhaps  at  a  temperature  equal  to  or  superior  to  that 
of  inflammation.  The  retard  of  inflammation  increases  with  dif- 
ference of  temperature  of  gas  and  that  of  inflammation  and  with 
the  increase  of  inert  gas.  This  latter  reason  explains  why,  accord- 
ing to  Davy,  a  bar  of  red-hot  iron,  though  above  650°,  will  not 
ignite  a  mixture  of  fire  damp.  By  opposing  circulation  one  may 
easily  provoke  inflammation  because  when  it  circulates  freely  the 
gas  does  not  remain  long  enough  exposed  to  the  temperature  of 
inflammation. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  5 

RATE  OF  PROPAGATION. 

Davy  is  recognized  as  the  first  to  study  the  question.  Without 
measuring  exactly  he  knew  it  took  less  than  one  second  for  the 
flame  to  travel  through  the  best  mixture  of  air  and  fire  damp  one 
foot  long,  and  also  came  to  the  conclusion  that  small  diameter 
tubes  and  metal  gauzes  will  prevent  passage  of  flame  of  the 
majority  of  mixtures.  *  , 

Bunsen  is  noted  as  having  found,  by  his  orifice  and  tank  method, 
the  figure  of  35  m.  per  second  for  H  and  O. 

MM.  Schloesing  and  De  Mondesir  did  some  unpublished  work 
for  gas-engines,  observing  in  glass  tubes  the  progress  of  the  flame. 
They  used  mixture  of  CO  where  r  is  so  slow  as  to  be  easily 
followed  by  the  eye.  They  noted  that  for  these  slow  mixtures 
an  agitator  such  as  that  of  the  jet  of  gas  into  a  quiet  mass  makes 
r  very  great  and  that  combustion  itself  causes  many  agitations, 
so  that  the  values  observed  may  vary  widely  and  be  always  dif- 
ferent from  normal.  The  agitations  are  due  to  :  ( i )  Difference  of 
density  between  burnt  and  unburnt  gases;  (2)  dilatation  of  burn- 
ing part;  (3)  vibratory  actions  of  several  kinds  due  to  compres- 
sibility of  gas  when  subject  to  impulses. 

M.  Fonesca  experimented  with  mixtures  of  O  and  various  gases 
that  burn  with  it.  A  stream  of  mixtures  is  given  a  high  velocity 
till  the  flame  cap  rests  some  distance  from  the  orifice ;  the  velocity 
is  then  reduced  till  contact  occurs  and  some  figures  deduced. 

H  +  O  35     m.  per  sec. 

CO  +  O  1.40 

C2H*  +  80  2.10 

PhH3  +  80  9.20 

M.  Gouy  tried  to  deduce  r  from  the  angle  of  the  luminous  cone 
in  Bunsen  flames.  Berthelot  and  Vieille  worked  on  the  subject 
and  found  the  rate  of  propagation  abnormal  and  extremely  high, 
for  certain  cases  moving  several  thousand  meters  per  second — 
very  superior  to  sound.  They  called  this  mode  of  propagation  the 
explosive  wave  and  recognized  that  the  wave  itself  must  travel 
with  the  velocity  of  sound. 

With  this  experience  to  guide  them  Mallard  and  Le  Chatelkr 
began  work.  Though  the  method  of  orifice  was  recognized  as 
introducing  many  errors  and  as  more  or  less  dangerous,  it  was 


THE  HEAT  ENGINE  PROBLEM. 


employed  for  mixture  where  r  did  not  exceed  one  meter  per 
second.  The  orifice  was  o.oi  m.  in  diameter.  The  second  method 
was  that  of  a  tube  closed  at  one  end  and  open  at  the  other  with 
ignition  at  the  open  end. 

Time  was  measured  by  automatic  machines — electric,  pneu- 
matic and  photographic.  The  electric  depended  on  a  passage  of 
a  spark  through  the  flame  when  gap  was  too  large  for  passage 
through  cold  gas.  The  pneumatic  depends  on  the  explosion  of 
gas  in  chambers  connected  with  the  tube  and  ignited  by  the  pas- 
sage of  the  flame.  The  photographic  consisted  of  a  moving  plate 
receiving  the  action  of  the  flame  in  a  glass  tube  giving  a  curve 
whose  abscissae  are  distances  in  tube  and  ordinates  time.  All 
these  methods  called  for  a  delicate  and  expensive  apparatus  and 
the  results  obtained  are  not  likely  to  be  soon  duplicated. 

It  was  found  that  various  influences  acted  to  change  the  rate 
of  propagation  and  figures  are  given  for  each. 

1.  The  material  composing  the  tube 

[CO  +  O]  in  .01  m.  tubes 

f  For  gflass  .  2.20  "1 

-{  y  m.  per  second. 

I  For  lead     .     .     .  2.35  J 

2.  Diameter  of  tubes  containing  the  mixture.    One  limit  is 

r=3.oo     m.  per  sec. 
D  =    .003  m. 

3.  The  temperature  of  the  mixture  H  and  air  with  30  per 


cent.  H. 


15° — 3.28  m.  per  sec. 


100 v 


4.35  m.  per  sec. 


4.  Nature   and   proportions   of   mixtures   in   tubes   .01    m.   in 
diameter : 


H  per  100. 

Velocity. 

C2  H4  per  zoo. 

Velocity. 

11.65  (CaH4)+jr. 

Velocity. 

6 

00 

5-6 

0.00 

-5.N 

.42 

IO 

.60 

6.0 

•03 

i.oN 

•30 

20 

J-95 

JO.O 

.42 

1.4  N 

.19 

30 
40 

3-30 

4-37 

12.0 
14.0 

.61 

.36 

.5C02 
i.  oo  CO2 

$ 

50 

3-45 

16.0 

.10 

60 

2.30 

16.2 

0.00 

70 

1.  10 

80 

o.co 

CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  7 

Illuminating  gas  and  air : 

Gas  per  100.  Velocity. 

10  .44 —  .48 

12  .68 .84 

15.0  1.02  —  I.OS 

17.5  1.16  —  i.2i 

20.0  .88  —  0.98 

H  and  O  give  rates  from  40  —  480  m.  All  the  above  concerns 
only  the  uniform  movement,  but  this  is  always  followed  by  the 
vibratory  movement  and  later  by  the  explosive  ware  if  the  mass 
be  large  enough  and  sufficiently  extended. 

A  summary  of  the  work  on  propagation  of  inflammation  brings 
out  the  following  facts : 

There  are  two  modes  of  propagation:  (i)  Normal,  that  by 
conductivity,  and  (2)  that  which  takes  place  by  the  transmission 
of  a  pressure  sufficiently  high  in  the  propagation  by  explosive 
wave.  These  correspond  to  deflagration  and  explosion  of  dyna- 
mite, etc.  Each  has  a  fixed  velocity  for  a  given  mixture  at  a 
given  pressure. 

R  due  to  normal  propagation  never  exceeds  20  m.  per  sec. 

For  H  and  air  the  maximum  is  4.30  m.  per  sec.  for  a  40  per  cent. 
H,  i.  e.}  an  excess  (30  per  cent.). 

For  C2H4  and  air  the  maximum  is  0.62  m.  per  sec.  for  a  12.2 
per  cent.,  i.  e.,  an  excess  (9.4  per  cent.). 

For  illuminating  gas  and  air  the  maximum  is  1.25  m.  per  sec. 
for  a  17.0  per  cent.,  i.  e.,  an  excess  (15  per  cent.). 

For  CO  and  O  and  air  the  maximum  is  2.00  m.  per  sec.  always. 

R  increases  with  I  and  when  tube  is  large  is  independent  of 
diameter,  but  a  tube  small  enough  may  cause  extinction. 

Agitation  increases  R.  Combustion  in  tube  with  slow  R  sets 
up  oscillation  which  may  cause  extinction. 

When  for  any  reason  of  vibration  or  explosion  of  burnt  gas 
the  pressure  transmitted  to  a  layer  next  is  equal  to  that  which 
would  elevate  it  to  the  temperature  of  inflammation,  the  com- 
bustion propagates  with  the  same  velocity  as  the  compressive 
wave  resulting  in  the  explosive  wave. 

TEMPERATURE  OF  COMBUSTION. 

Dulong,  Favre  and  Silberman,  Thomsen  and  Berthelot  all 
worked  on  Q,  from  which  the  temperature  of  combustion  was  to 


8  THE    HEAT    ENGINE    PROBLEM. 

be  calculated  with  a  known  value  of  Cv  the  specific  heat.  But 
Saint  Claire  Deville  showed  that  dissociation  could  take  place. 
He  tried  dropping  hot  metal  from  the  flame  to  water.  Crova  and 
Rosetti  used  optical  methods  on  flames.  Vieille  used  spherical 
bombs  and  noted  displacement  of  piston  to  get  maximum  pres- 
sures. 

Bunsen,  among  others,  tried  to  compute  the  temperature  of 
combustion  from  observed  values  of  pressures  resulting  from 
explosion.  Some  of  the  pressure  ratios  determined  by  him 
follow : 


Gas  Added  to  i  Volume  of 


Explosive  Mixture.  For  Mixtures  of  H. 

O  9-97 

o  975 

I.26N  7.49 

6 

Gas  Added  to  i  Volume  of  p± 

Explosive  Mixture.  For  Mixtures  of  CO. 

o   ..............................  .  ........  10.78 

o   .......................................  10.19 

.io8O    ...................................  9.05 

.686CO   ..................................  8.89 

.8550    ...................................  8.44 

i.o86O    ....................  ........  .......  7-86 

I.2S6N    ...................................  7-73 

I.256N    ...................................  7-35 

i.7iO    ....................................  6.67 

2.i6O    ....................................  5-83 

4-79 


RESUME  OF  TEMPERATURE  OF  COMBUSTION 
Pressures  developed  are  higher  than  the  static  due  to  the  heat 
developed.     Before  communicating  itself  to  the  whole  mass  the 
increase  of  pressure  concentrates  itself  on  the  layer  in  contact 
and  the  effect  is  greater  the  greater  the  rate  of  propagation. 
Permanent  gases  cool  according  to 

dd 

^dt=ae  +  be 

when  e  is  (temperature  of  gas)  —  (temperature  of  walls)  ; 
a  is  independent  of  pressure. 
b  is  inversely  proportional  to  density. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  9 

If  the  gas  can  condense  the  fall  in  pressure  is  given  by 

dw 

dt  "  ~~  ^°'' 

^v  is  the  variable  pressure. 

p0  is  tension  of  the  vapor  at  temperature  of  the  walls. 

When  gas  is  partially  condensable  we  have 

I       dw 

where  w  is  the  variable  pressure  and  p0  is  pressure  of  whole  mix- 
ture at  temperature  of  walls. 

Dissociation. — Information  from  cooling  curves.  Dissociated 
CO2  will  recombine  when  mean  temperature  of  gas  reaches  1800°. 
Gases  mixed  with  it  have  apparently  no  effect.  No  dissociation 
of  H2O  noticed. 

Temperature  of  Combustion  at  Constant  Volume. — Calculated 
from  pressures  when  dissociation  =  o,  i.  e.,  from  pressure  ratios. 

Specific  heats  are  found  by  the  method  noted  to  follow  closely 

these  formulae 

£. 

0°  —  2000° 


€,,  =  4.74 

For  H2O         Cv  =  5.61  -f  3.28  Tio- 
Perfect  gases  Cv  =  4.8  -f  .0006  T 


6.3—13.6 

5.6 —  12.2 
4.8  —  6.0 


Temperatures  of  combustion  at  constant  pressure  are  calculated 
by  making  change  in  the  value  for  specific  heat. 

After  these  facts  were  obtained  there  has  appeared  periodically 
attempts  at  development  of  special  points.  Dugald  Clerk  obtained 
some  pressures  due  to  explosion,  and  more  recently  others,  includ- 
ing the  Massachusetts  Institute  of  Technology,  have  given 
some  values  of  pressure  ratios  for  mixtures  of  fuel  and  air,  but 
the  results  do  not  always  agree  and  seldom  cover  working 
conditions. 

After  all  the  work  is  looked  over  and  the  labor  and  expense 
attached  to  the  results  realized  it  seems  rather  a  pity  that  we  have 
nothing  of  any  immediate  value  for  the  designer  of  gas-engines  or 
the  user  of  explosive  mixtures  in  other  fields.  For  example,  it 


10  THE    HEAT    ENGINE    PROBLEM. 

is  absolutely  impossible  to  calculate  the  maximum  pressure  that 
may  result  in  a  cylinder  of  a  gas-engine,  even  when  the  composition 
of  the  gas  is  known,  or  secondly  to  determine  the  change  in  vol- 
ume due  to  the  combustion  of  a  mixture  at  constant  pressure. 
Of  course  a  calculation  can  be  made,  but  it  will  be  far  from  that 
realized  by  actual  trial  and  the  reason  can  no  doubt  be  found 
in  the  great  complexity  of  the  process  involving  many  unknown 
influences. 

As  another  illustration  of  the  unavailable  form  of  much  of 
the  present  information  and  apparatus  there  may  be  cited  the 
case  of  determining  data  for  the  mean  effective  pressure  that 
must  be  counted  on  in  designing  an  exploding  gas-engine. 

Assuming  the  compression  and  expansion  lines  as  constant 
curves  the  mean  effective  pressure  of  an  Otto  cycle  card  will 
depend  on  the  compression,  i.  e.}  cylinder  clearance,  and  on  the 
length  of  the  explosion  line,  i.  e.,  on  kind  of  fuel  and  composition 
of  mixture.  From  the  clearance  can  be  computed  the  amount 
of  burnt  or  partly  burnt  gases  that  will  be  mixed  with  a  fresh 
charge,  and  the  resulting  complex  mixture  will  have  a  certain 
pressure  range  for  its  explosion  and  this,  moreover,  for  that  mix- 
ture must  be  constant.  But  with  the  information  at  hand  this 
question  fundamental  to  engineers  designing  gas-engines  cannot 
be  computed. 

The  questions  set  down  for  clarification  are  these : 

1.  Pressures  resulting  from  constant  volume  combustion  of  a 
mixture  of  gas  with  air  in  all  explosive  proportions  to  determine 
(a)  best  mixtures  and  compare  with  chemical  determinations  of 
the  same,  and  (b)  the  maximum  pressure  for  each  mixture  with 
variation  due  to  change  of  composition. 

2.  Volumes   resulting   from   constant  pressure  combustion   of 
mixtures. 

3.  Heat  of  combustion  of  these  mixtures  burnt  at  constant 
pressure. 

4.  Heat  of  combustion  for  constant  volume  combustion. 

5.  The  effect  of  dilution  by  products  of  combustion  on  all  of 
these  quantities. 

These  questions  called  for  the  design  of  apparatus : 

1.  For  measuring  air,  gas  and  neutral  products  of  combustion. 

2.  For  mixing,  compressing  and  storing  mixtures. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  II 

3.  For  producing  products  of  combustion  by  methods  available 
for  determinations  on  an  engineering  scale. 

4.  A  constant  pressure  combustion  calorimeter  for  explosive 
mixtures. 

5.  Same  for  constant  volume. 

6.  A  chamber  for  determining  pressures  due  to  explosion. 

7.  A  chamber  for  determining  volume  increase  due  to  constant 
pressure  combustion. 

With  the  apparatus  at  hand  there  are  few  of  the  questions  vital 
to  engineers  entering  into  the  thermal  properties  of  explosive 
gaseous  mixtures  that  cannot  be  determined  in  a  way  immediately 
available,  i.  e.}  without  computation,  for  use  in  design.  It  must 
be  noted  that,  while  many  of  the  actions  and  processes  are  complex 
and  a  pure  scientist  would  be  bound  to  analyze  them  and  assign 
to  each  element  a  value,  the  engineer  is  more  concerned  with 
resultant  effects  than  elemental  ones,  and  is,  moreover,  saved  the 
possibility  of  multiplied  error  in  computing  the  resultant  from 
the  elemental  if  the  resultant  can  be  measured  directly  with  suffi- 
•cient  known  conditions  to  insure  constancy  and  serve  as  a  specifica- 
tion for  the  process. 


SOME  NEW  WORK  ON  PROPERTIES  OF  EXPLOSIVE 

MIXTURES. 

THE  APPARATUS. 

All  work  in  the  experimental  study  of  heat  is,  as  is  well  known, 
very  difficult,  calling  for  most  careful  observations  with  apparatus 
sometimes  impossible  to  construct  with  sufficient  accuracy,  and 
always  expensive  even  to  a  slight  degree  of  accuracy.  The 
study  of  the  characteristics  of  explosive  mixtures  is  no  exception 
to  the  rule,  partaking  of  the  general  difficulty  of  all  heat  work, 
that  of  isolation  of  phenomena  of  observation,  and  the  prevention 
of  the  manifestation  of  more  than  one  at  a.  time.  In  most  cases 
each  experimenter  has  designed  and  constructed  apparatus  of  his 
own,  and  in  no  case,  it  seems,  has  any  one  used  instruments  first 
employed  by  a  predecessor.  It  is  probably  due  to  this  that  the 
results  of  different  observers  do  not  always  agree.  In  none  of 
the  researches  does  there  seem  to  have  been  adopted  a  sufficiently 
direct  and  simple  means  for  obtaining  ALL  the  results ;  having  an 
instrument  to  measure  one  constant  the  observer  has  rested  con- 
tent with  COMPUTING  others  equally  important,  which  were  mathe- 
matically related,  though  these  computed  values  might  also  have 
been  observed  directly.  As  actual  trial  has  shown  that  the  results 
obtained  by  this  process  of  computation  of  constants  from  ob- 
served values  of  some  other  related  constant  is  not  always  reliable, 
introducing,  as  it  generally  'does,  a  multiplied  error  if  not  involving 
unproved  assumptions  of  interrelation,  it  seemed  desirable,  (i), 
that  each  constant  needed  be  measured  directly  under  well-defined 
conditions,  and  (2),  that  the  apparatus  for  the  measurements  be 
made  simple  enough  for  duplication  by  others  whose  observations 
could  act  as  a  check  on  the  results.  In  this  reduction  to  simplicity 
it  is  essential  that  the  apparatus  be  so  constructed  as  to  permit  of 
measurements  on  the  mixtures  under  as  nearly  the  same  condi- 
tions as  found  in  engineering  practice  as  was  possible.  Such  a 
set  of  apparatus  once  set  up  in  a  laboratory  can  be  used  to  rapidly 
determine  what  is  wanted  from  time  to  time  as  occasion  might 
demand,  and  the  results  could  easily  be  checked  up  by  other  ob- 

12 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  13 

servers  on  the  same  or  duplicated  apparatus.  The  actual  construc- 
tion should  involve  little  or  no  machine  work,  and  the  instruments 
of  observation  must  be  those  in  common  use  in  the  general  engi- 
neering laboratory. 

The  results  of  the  work  on  continuous  explosive  combustion  of 
gaseous  mixtures  furnished  a  ready  means  for  obtaining  burnt 
gases  for  dilution  of  mixtures  of  otherwise  known  composition 
of  air  and  gas.  The  action  and  appearance  of  the  fire  itself  fur- 
nishes a  very  good  and  simple  means  for  determining  the  propor- 


FJG.  i. 

tions  being  fed,  and  hence  the  character  of  the  products  of  com- 
bustion, whether  oxidizing  reducing  or  neutral,  within  limits  pretty 
close ;  much  closer  than  we  can  attain  to  constancy  in  gas-engine 
work. 

For  a  constant  pressure  combustion-calorimeter  this  same 
method  also  filled  requirements.  For,  as  has  been  shown,  a  mix- 
ture of  air,  gas  and  neutral  in  any  proportions  that  can  be  exploded 
may  be  burnt  in  a  closed  chamber  and  under  pressure,  so  there 


14  THE    HEAT   ENGINE   PROBLEM. 

only  remains  as  a  necessity,  the  provision  for  measuring  gas  burnt 
and  heat  developed  by  submerging  the  whole  apparatus  in  water. 
The  details  of  this  calorimeter  as  adopted  and  used  will  be  noted 
later. 

Gas  measuring,  mixing  and  storing  was  accomplished  by  water 
displacement  in  thin  metal  tanks ;  the  quantities  read  by  the  levels 
in  a  water  glass  before  and  after  more  water  had  displaced  the  gas 
required.  All  connections  and  communications  between  the  parts 
were  made  of  combinations  of  pipe  fittings  and  rubber  hose.  Four 
tanks  were  provided.  (Fig.  I,  A,B,C,D),  each  fitted  with  water 
inlet  and  discharge  communicating  with  water  main  and  sewer, 
and  each  fitted  also  with  gas  inlet  communicating  with  the  appro- 
priate source  and  discharges  connecting  A,  B,  and  C  with  D  and 
that  of  D  with  the  apparatus  in  which  mixtures  were  to  be  used. 
The  first  three  tanks  then  were  measuring  tanks,  A,  for  illuminat- 
ing gas,  B,  for  air,  and  C  for  products  of  combustion  prepared  pre- 
viously, while  the  fourth,  D,  is  the  mixing  and  storage  tank  and  is 
the  only  one  in  which  the  pressure  was  allowed 
to  exceed  atmosphere.  Two  glass  tubes,  E 
and  F,  were  provided  to  each  of  the  measuring 
tanks  and  extending  the  entire  length.  One 
of  these  tubes,  F,  was  connected  by  both  ends 
to  the  interior,  while  the  other,  E,  was  con- 
nected at  the  bottom,  only  the  top  being  open 
to  atmosphere,  Fig.  2.  The  doubly  connected 
tube  then  serves  as  an  ordinary  water  column 
showing  the  water  level,  while  the  other 
gives  an  indication  of  the  interior  pres- 
FlG  2  sure.  When  the  level  of  the  open  column  is 

equal  to  that  in  the  closed  column  the  pressure 
on  the  interior  is  atmosphere ;  if  the  level  of  the  open  column  rises 
above  that  of  the  closed  column  then  the  interior  pressure  exceeds 
atmosphere  by  an  amount  exactly  equal  to  that  due  to  difference 
of  level. 

To  obtain  a  mixture  of  any  composition  the  method  of  operation 
was  as  follows:  All  tanks  were  filled  with  water  till  they  over- 
flowed; then,  one  at  a  time,  the  water  was  allowed  to  flow  out 
of  the  measuring  tanks  A,  B,  C  and  illuminating  gas,  air  and 
products  of  combustion,  flowing  in  each  to  its  own  tank,  filled  the 


CYCLIC   ANALYSIS    OF    HEAT    ENGINES.  15 

space  left  by  the  receding  water.  Manipulation  of  the  gas  dis- 
charge and  water  inlet  valves,  guided  by  the  relative  position  of 
the  water  levels  in  the  two  columns,  enabled  the  operator  to  keep 
the  pressure  on  the  inside  equal  to  atmosphere,  and  relieving  the 
walls  of  any  stress  as  well  as  preventing  compression  or  rarefica- 
tion  of  the  gas.  When  each  tank  is  filled  with  its  respective  gas 
the  amounts  of  each  desired  in  the  mixture  are  laid  off  on  the 
water  glass  above  the  present  water  level  and,  as  these  have  all 
the  same  diameter,  the  height  on  the  columns  will  be  a  measure 
of  the  quantity  of  the  gas.  Water  is  then  turned  out  of  the  storage 
tank  D  and  a  partial  vacuum  created  therein.  With  one  hand  on 
the  gas  cock  x  and  the  other  on  the  water  cock  yf  the  amount  of 
gas  wanted  is  caused  to  flow  from  tank  A,  where  it  was  measured, 
to  the  tank  D,  where  it  is  wanted,  the  transfer  being  made  without 
allowing  any  change  of  pressure  in  tank  A  by  simply  regulating 
the  relative  openings  of  the  valves  x  and  y  and  watching  the  two 
water  columns.  After  the  gas  wanted  is  transferred  air  is  simi- 
larly measured  and  transferred,  and  later,  if  desired,  products  of 
combustion,  until  finally  the  tank  D  contains  all  the  constituents 
of  the  desired  mixture.  All  openings  to  D  are  then  closed  and 
water  from  the  main  G  admitted  through  the  three-way  cock  H, 
until  the  full  pressure  (in  this  case  60  Ibs.  gauge)  has  compressed 
the  mixture.  This  method  of  feeding  and  afterward  compressing, 
results  in  a  perfectly  uniform  mixture,  as  was  proved  by  com- 
paring effects  derived  from  burning  parts  first  drawn  off  with  the 
last  that  remained. 

We  have  now  in  tank  D  a  perfectly  uniform  mixture  of  known 
composition,  compressed  to  60  Ibs.  and  available  for  whatever 
tests  or  experiments  we  may  desire  to  make,  by  the  simple  opening 
of  the  valve  /.  All  this  measuring,  transferring  and  compressing 
the  constituents  of  the  mixture  takes  about  five  minutes  from  the 
beginning  up  to  the  time  the  mixture  is  ready  for  use.  When  the 
operator  is  working  with  one  mixture  this  time  may  be  lessened  if 
an  assistant  is  at  hand  to  recharge  measuring  tanks  and  get  the 
quantities  desired  measured  off  for  the  next  mixture  desired. 

NEUTRAL  GAS  GENERATOR. 

To  generate  neutral  products  of  combustion  a  positive  blower 
A,  Fig.  3,  driven  by  a  Crocker- Wheeler  motor  B,  fed  an  ex- 


i6 


THE    HEAT   ENGINE   PROBLEM. 


plosive  mixture  of  air  and  gas  to  the  two-inch  tee  C.  The  propor- 
tions were  obtained  as  desired  by  air-cock  D  and  gas-cock  E  on 
the  blower  suction  and  the  mixture  thus  obtained  burned  within  the 
mass  of  broken  magnesite  in  the  tee  C.  Ignition  was  effected 
through  the  opening  G,  and  when  the  proportions  were  found 
correct  by  observing  the  fire  this  opening  was  closed,  thus  sending 
the  products  of  combustion  over  through  pipe  /  to  bell  K  under 


FIG.  3. 

water  in  tank  L.  When  wanted  the  products  of  combustion  could 
be  drawn  off  from  K  through  pipe  M  under  a  constant  pressure, 
being  that  due  to  the  height  of  water  above  the  bell.  More  gases 
than  were  wanted  were  continuously  generated,  the  surplus  always 
bubbling  off  from  bell  K;  this  was  to  insure  getting  fresh  gases 
delivered  at  constant  and  small  head.  The  water  around  the 
pipes  served  to  condense  and  catch  any  steam  in  the  products. 

CONSTANT  PRESSURE  COMBUSTION  GAS  CALORIMETER. 
The  constant  pressure  calorimeter  consisted  of  a  one-half-inch 
tee  F,  Fig.  4,  nearly  full  of  broken  magnesite  and  fitted  with  a 
jump-spark  plug  G  operated  by  a  vibratory  primary  circuit  breaker 
induction  coil.  Explosive  mixtures  of  the  previously  determined 
composition  and  of  known  amount  were  fed  to  the  bottom  of  the 
combustion  chamber  F  through  a  one-eighth-inch  copper  tube  E. 
As  it  was  necessary  to  discharge  the  whole  of  the  measured 
quantity  of  mixture  from  the  pressure  tank  Df  and  necessary 
secondly  that  no  water  should  follow,  the  trap  B  was  introduced. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  I/ 

It  is  simply  a  glass  bottle  with  two  glass  tubes,  one  a  feed  and  the 
other  discharge,  fitted  to  a  perforated  cork.  The  discharge  tube 
was  connected  with  the  calorimeter  by  the  light  rubber  tube  D. 
Hot  gases  from  F  were  discharged  through  H  to  the  bottom  of 
the  water  tank  and  thence  passed  up  through  square  coil  of  one- 


FIG.  4. 

eighth-inch  iron  pipe.  The  end  of  this  coil  was  supplied  with 
rubber  and  glass  tubes,  so  that  the  products  of  combustion  could 
be  directed  to  the  atmosphere  or  to  any  point  of  the  water  to  act 
as  a  stirrer  when  so  desired. 

CONSTANT  VOLUME  COMBUSTION  PRESSURE  RATIO  CHAMBER. 

The  explosion  chamber  for  determining  the  pressures  due  to 
constant  volume  combustion  consisted  primarily  of  tee  A,  Fig.  5, 
nipples  B  and  caps  C,  C .  A  Crosby  gas-engine  indicator  was 
attached  to  the  tee  as  shown.  The  spark  plug  D  was  carried  in 
one  branch  of  the  three-way  cock  on  top  and  on  other  branch 
was  connected  to  mixture  feed  and  water  overflow  openings  E. 
The  apparatus  was  first  filled  with  water  through  valve  F  until  it 
overflowed  through  valve  G,  the  mixture  feeding  valve  H  and 


18 


THE    HEAT    ENGINE    PROBLEM. 


water  discharge  valve  /  being  closed ;  the  spark  points  meantime 
being  protected  from  the  water  by  the  three-way  cock.  When 
entirely  full  of  water  valves  G  and  F  are  closed  and  H  and  / 
opened,  the  mixture  from  tank  D  thus  expelling  the  water;  the 
three-way  cock  is  then  thrown  to  permit  contact  of  points  with 


FIG.  5. 

mixture,  which  is  allowed  to  blow  through  freely  to  fill  chamber 
at  atmospheric  pressure.  Then  all  openings  are  closed  and  the 
mixture  fired,  the  pressure  rise  being  shown  by  the  length  of  line 
drawn  on  the  indicator  drum  to  the  proper  scale.  To  expel  the 
burnt  gases  water  is  admitted  as  before  and  the  new  charge  sub- 
sequently used  to  drive  the  water  out. 

CONSTANT  PRESSURE  COMBUSTION  VOLUME  RATIO  APPARATUS. 

The  quantity  of  gas  that  could  be  stored  in  the  tank  D  is  so 

small  and  the  time  to  attain  maximum  effect  in  a  heating  chamber 


CYCLIC    ANALYSIS   OF    HEAT    ENGINES. 


so  long,  that  with  these  tanks  the  combustion  chamber  could  not 
become  heated  sufficiently  to  make  a  measurement  of  maximum 
volume  increase.  The  apparatus  of  Fig.  6  was  constructed  with 
this  end  in  view.  It  depends  for  its  action  on  the  principles  of 
gas  flow  through  an  orifice.  The  rate  of  flow  of  a  gas  through 
an  orifice  is  proportional  to  the  form  of  orifice  and  to  the  pressure 
drop  through  the  orifice.  Now  if  the  gas  be  caused  to  pass 
through  a  hole  in  a  plate  before  combustion,  and  later,  after  com- 
bustion, pass  through  a  similar  hole  in  a  similar  plate,  the  constant 
.due  to  the  form  of  orifice  would  be  eliminated  in  comparing 
velocities  through  the  two  holes.  Secondly,  when  the  fall  in 
pressure  through  each  hole  is  the  same  the  velocity  of  flow  through 
each  plate  will  be  equal,  and  the  volume  passing  will  be  propor- 


FIG.  6. 

tional  to  the  area  of  the  orifice  only  if  the  pressures  used  be  small 
enough  to  make  correction  for  compression  vanishingly  small. 
Gas  and  air  are  mixed  in  any  proportion  desired  at  the  compressor 
intake  and  delivered,  mixed,  to  the  chamber  AB,  from  which  the 
mixture  will  pass  to  the  upper  chamber  C  through  a  hole  in  the 
plate  secured  between  the  flanges.  In  chamber  C  there  is  placed 
a  cone  of  brick  to  keep  lower  plate  cool,  and  in  the  cone  broken 
rock  to  permit  of  the  combustion  of  the  explosive  mixture.  The 
top  plate  between  the  flange  D  is  provided  with  asbestos  sheets 
to  keep  the  hot  gases  from  chilling  just  before  issuing. 

At  times  both  the  brick  cone  for  the  lower  and  the  asbestos  sheet 
protection  for  the  upper  plates  were  removed  for  the  taking  of 


20 


THE    HEAT    ENGINE    PROBLEM. 


observations,  while  at  another  time  a  one-inch  lining  of  fire  clay 
was  supplied  to  prevent  radiation.  Mercury  manometers  to  both 
chambers  indicate  the  interior  pressures,  and  hence  the  drop  in 
pressure  through  each  plate. 

RESULTS  OBTAINED  WITH  APPARATUS.     FLAMES  IN  ATMOSPHERE 

OF  DIFFERENT  AIR-GAS  MIXTURES. 

Before  proceeding  to  the  effects  of  the  combustion  of  different 
mixtures  it  is  necessary  to  first  determine  the  limits  of  combusti- 
bility, and  in  so  doing  opportunity  was  afforded  to  observe  the 
characteristics  of  the  flames  of  different  mix- 
tures. 

The  mixture  from  the  compression  storage 
tank  D  was  led  to  the  apparatus,  Fig.  7.  This 
consisted  of  a  one-quarter-inch  tee  with  a 
valve  A  and  manometer  B,  the  flame  locating 
at  C.  Mixtures  were  ignited  and  the  flow 
regulated  to  determine  the  maximum  length 
and  character  of  the  flame  and  the  pressure 
at  which  the  flame  would  blow  off. 

Appearance  and  blozv-off  pressures  of  mix- 
tures of  air  and  gas  burnt  at  opening  of  one- 
quarter-inch  pipe  in  atmosphere  of  air: 


Mixture,  {Air    . 


FIG.  7 


Blow-off  pressure,  1.25"  H2O 

With  a  length  of  one-half  inch  a  clear  blue  flame  results;  an 
increase  to  three  inches  in  length  develops  a  green  core  and  faint 
spots  of  yellow  appear.  A  still  further  increase  of  the  pressure 
causes  the  core  to  become  less  distinct  and  the  end  of  the  flame 
becomes  wavy  and  oscillatory.  A  roaring  noise  develops  also. 
Just  before  blow-off  the  flame  becomes  violet  and  green  near 
nozzle ;  the  end  is  quite  wide  and  spreading.  Blow-off  occurred 
at  1.25  inches  of  water  pressure  with  a  length  of  fourteen  inches 
after  some  trembling  at  the  nozzle. 

Mixture,  j  ^ir    '     '     '  2\  Blow-off  pressure,  .8"  H2O. 

(^  vJclS       •        •        •     JL    ) 

Flame  all  blue  and  remained  blue  as  length  was  increased  with 


CYCLIC   ANALYSIS   OF    HEAT    ENGINES.  21 

very  much  less  spreading  at  the  ends.  There  appeared  no  core. 
A  length  of  twelve  inches  was  the  maximum  at  a  water  pressure 
of  eight-tenths  of  an  inch. 


Mixture,   {  ^ir    '     '     '  3  }  Blow-off  pressure,  .5"  H2O. 

(.  vjraS      •       .       •    I    ) 


,   j  ^ir    '     *     '  5  }  Blow-off  pressure,  .12"  H2O. 
(,  vjas    •     •     .  i  ) 


First  appearance  of  the  flame  cap,  which  was-  of  yellowish  color 
surrounded  by  light  blue  and  could  be  extended  to  a  maximum 
length  of  six  inches  with  a  blow-off  pressure  of  one-half  inch 
water.  The  cap,  however,  instead  of  being  smooth,  had  serrated 
edges. 

Mixture,  j  ^ir    *     '     '  4  1  Blow-off  pressure,  .3"  H2O. 
v.  vjas    .     .     .  i  ) 

The  flame  cap  is  now  more  distinct,  with  a  filmy  halo  surround- 
ing it,  color  blue-green.  The  flame  on  extension  becomes  sharply 
pointed  at  the  end  with  little  vibration.  At  the  maximum  length 
of  four  inches  and  blow-off  pressure  of  three-tenths  of  an  inch 
the  flame  became  very  pale. 

Mixture, 

The  flame  was  very  similar  in  appearance  to  the  last  with  the 
exception  of  being  more  blue  than  green,  the  tip  was  very  pale 
and  sharp-pointed  at  the  maximum  length  of  three  and  one-half 
inches. 

Mixture,    |g£    '     '     '  ^  j  Blow-off  pressure,  .08"  H2O. 

Flame  was  somewhat  shorter  and  somewhat  more  filmy  or 
cloudy  in  character,  the  maximum  length,  of  a  little  more  than 
two  inches  was  reached  with  a  water  pressure  of  about  eight 
one-hundredths  of  an  inch. 

Mixtures  containing  more  air  than  the  last  could  not  be  burnt. 

The  limits  of  explosive  combustibility  differ  from  the  preceding 
limits  for  flames.  When  admitted  to  the  explosion  chamber, 
isolated  and  exploded  in  bulk  the  limits  of  combustibility  were  : 

Air         .     .  3  )         ^  f  Air    ...  7. 
Gas   .    .    .  i  jUpt°iGas    .    .    .  i. 

But  with  the  mixtures  6.5/1  up  to  7/1  the  ignition  was  very 
uncertain,  occurring  only  after  long  passage  of  the  spark  and 


22  THE    HEAT    ENGINE    PROBLEM. 

often  failing  entirely.  This  is  an  unfailing  characteristic  of 
extremely  dilute  mixtures,  i.  e.,  mixtures  containing  a  large  per- 
centage of  neutral  or  excess  gases. 

Constant  Pressure  Combustion  Calorimeter. 

Before  stating  the  results  of  this  calorimeter  on  an  unanalyzed 
water  gas  it  will  be  well  to  look  at  some  characteristics  of  a  water 
of  typical  composition.  It  is  intended  that  this  calorimeter  be 
used  by  men  unskilled  in  gas  analysis  and  in  places  where  such 
an  apparatus  is  unavailable.  The  results  that  theoretically  should 
accrue  from  this  typical  water  gas  will  be  compressed  until  what 
was  actually  observed  on  the  action  of  the  gas  used. 

Stillman  gives  as  an  ordinary  water  gas  the  following  mixture: 

C02 3-8 

C2H,   14.6 

CO    28.0 

H  35-6 

CH4  16.7 

N   1.3 

Total    100.0 

of  this  we  have 

NEUTRAL. 

C02   3-8 

N   ^3 

Total    5-i 

This  gas,  moreover,  will  heat  yield  691.59  B.  T.  U.  per  cubic 
foot  products  condensed,  and  will  call  for  in  its  combustion  5.21 
parts  of  air  per  one  part  of  gas. 

A  chemical  mixture  then  would  have  these  characteristics : 

Air    ' 5-21    volumes 

Gas LOO 

Total    6.21 

of  which  we  have 

Neutral  {Neutral  in  gas     .051 
I  Nitrogen  in  air  4120 

Total  neutral  4.17  in  6.21  parts  or  67  per  cent,  neutral. 

Let  us  then  tabulate  various  mixtures  and  note  some  of  their 
characteristics. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES. 


Gas. 

i 

i 

i 

i 

i 

i 

i 

I 

I 

Air. 

3.o 

3-5 

4-0 

4-5 

5-o 

5-5 

6.0 

6.5 

7-o 

Inactive  Air,  i.  e.,  Excess. 

.29 

.79 

1.29 

1.79 

Active  Air. 

3-o 

3-5 

4.0 

4-5 

5-o 

5.21 

5.21 

5.*i 

5-21 

Inactive  Gas,  i.  e.,  Excess. 

.427 

.328    .232 

•135 

.050 

Active  Gas. 
Neutral  in  Active  Air. 
Neutral  in  Active  Gas. 

•  573 
2.372 
.029 

.672 
2.768 
•034 

.768 
3-163 
•039 

.865 
3-559 
•044 

•950 
3-954 
.048 

I.OOO 

4.120 

.051 

I.OOO 

4.120 

.051 

I.OOO 

4.120 

.051 

I.OOO 

4.120 

.051 

Total  inactive  or  excess. 
Per  cent,  inactive  or  excess. 

2.828 
.701 

3-  '3°!  3-434 
.696    .687 

3-735 
.680 

4.052 
•675 

4.461 

.686 

4.96! 
.704 

5.46! 
.729 

5-961 
.746 

It  should  be  noted  how  very  slightly  the  increase  in  percentage 
of  dilution  increases  with  the  excesses  of  air  and  gas ;  though  the 
proportions  may  vary  over  100  per  cent.,  the  dilution  varies  through 
but  little  more  than  5  per  cent.  This  is  very  striking,  as  will  be 
noted  again  when  the  results  of  increasing  dilution  by  neutral 
additions  is  taken  up.  There  can  be  little  doubt  that  the  limits 
of  combustibility  is  intimately  associated  with  the  per  cent,  of 
neutral  or  inactive  gases  present. 

Next  let  us  examine  the  calorific  values  of  some  of  these  mix- 
tures, i.  e.j  the  amount  of  heat  that  one  cubic  foot  of  gas  can 
deliver  when  burnt  explosively  in  mixtures  within  the  limits  of 
explosive  combustion.  The  heat  developed  by  a  cubic  foot  of  the 
gas  in  question  is  691.59  B.  T.  U.  when  completely  burnt,  *.  e.f 
in  a  chemical  mixture,  or  in  a  mixture  in  which  air  is  in  excess, 
within  of  course  the  limits  of  combustibility. 


Gas. 

i 

i 

i 

i 

i 

i 

I 

I 

I 

Air. 

3-o 

3-5 

4.0 

4-5 

5-o 

5-5 

6.0 

6.5 

7-o 

Gas  Burnt,  i.  e.,  Gas  that  could 
find  Air  Enough  to  Burn  it. 
B.  T.  U.  Available. 

•573 
396.3 

.672 
464.8 

.768 
53L2 

.865 
598.2 

•950 
657.0 

I.OOO 

691.6 

I.OOO 

691.6 

I.OOO 

691.6 

I.OOO 

691.6 

These  results  are  shown  graphically  on  the  curve  A  of  Fig.  9. 
Curve  B  shows  the  results  of  observations  on  the  water  gas  used 
in  the  calorimeter  and  of  unknown  composition. 

The  calorimeter  can  was  filled  with  16.5  Ibs.  water  for  each  run 
and  the  water  equivalent  determined  by  experiment  to  be  2.1  Ibs. 
of  water ;  this  is  for  both  can  and  coil.  Radiation  was  assumed 
zero,  as  the  temperature  of  the  room  was  in  every  case  between 
the  initial  water  temperature  and  the  final. 


24 


THE    HEAT   ENGINE   PROBLEM. 


Four  inches  altitude  of  gas  was  used  every  time  from  the  eigh- 
teen-inch  tank  mixed  each  time  with  varying  quantities  of  air. 
The  results  are  as  follows  reduced  to  cubic  feet  of  gas : 

B.  T.  U.   PER  CUBIC  FOOT  OF  GAS  WHEN   MIXED  WITH  AIR. 


Gas. 


700 


Air. 

3-0 

3.5 

4.0 

4-5 
5-0 
5-5 
6.0 

6-5 


B.  T.  U.  per  cu.  ft.  Gas. 
27S.I 
347.82 

401.57 
471.00 
541.70 
6l6.59 
600.78 


powers  of 


bo 


7oo 


400 


\ 


,00 


ir  |3er  One 

FIG.  9. 

This  is  one  set  of  readings,  and  the  curve  is  a  very  good  one. 
other  sets  of  readings  were  taken,  and  if  the  results  had  been  re- 
duced to  a  mean  the  curve  would  have  been  perfect.  The  one  set 
given  were  obtained  in  a  space  of  about  two  hours.  The  values 
for  mixtures  6.5/1  and  7/1  were  very  erratic  but  always  below 
the  maximum,  and  this  result  is  extremely  important,  viz.,  that 
very  dilute  mixtures  after  combustion  has  been  started  may  cease 
to  burn  before  combustion  has  become  complete. 


CYCLIC    ANALYSIS    OF    HEAT    ENGINES.  25 

It  may  be  well  to  note  a  few  peculiarities  of  this  calorimeter 
before  leaving  the  subject.  When  starting  a  continuous  stream  of 
sparks  is  provoked  between  the  points  and  the  mixture  then  turned 
on.  As  soon  as  the  flame  cap  has  settled  and  combustion  is  well 
started  the  spark  may  be  turned  off  and  attention  turned  to  watch- 
ing the  thermometer  and  directing  the  stirring  of  the  water.  The 
feed  may  be  depended  upon  to  take  care  of  itself.  The  process  of 
starting,  however,  will  not  be  successful  unless  good  judgment 
in  regard  to  certain  points  is  exercised;  however,  a  few  trials 
are  sufficient  to  show  up  these  difficulties,  and  the  means  for  avoid- 
ing them. 

If  the  entering  stream  be  so  small  in  quantity  as  to  give  the  gas 
too  small  a  velocity  through  the  feed  pipe,  then  when  the  first  part 
of  the  mixture  reaches  the  spark  there  will  be  back-flashing,  which 
may  result  in  a  succession  of  explosions.  These  successive  ex- 
plosions will  have  a  period  depending  on  the  velocity  of  feed; 
they  become  more  frequent  as  the  velocity  increases,  until  finally 
the  velocity  becomes  high  enough  to  force  the  flame  beyond  the 
feed  pipe,  when  it  will  lodge  in  the  rocks  and  stay  there.  It  may 
even  happen  that  the  back-flash  will  extend  to  the  trap,  but  no 
harm  will  be  done  except  blowing  off  the  rubber  tube  and  causing 
a  loss  of  the  charge.  At  first  this  back-flashing  was  very  trouble- 
some and  necessitated  investigation.  When  the  combustion  cham- 
ber and  coil  were  removed  from  the  water  no  back-flash  occurred 
even  with  a  very  slow  feed,  but  a  reinsertion  caused  the  trouble 
to  reappear.  This  was  attributed  to  the  intermittent  back  pres- 
sure effect  of  the  bubbling  of  discharging  gas  through  the  water; 
it  was  then  the  flexible  end  to  the  coil  was  attached  so  that  the 
discharge  could  be  directed  above  during  and  below  after  starting, 
when  it  would  do  no  harm.  Since  it  was  now  shown  that  back 
pressure  could  have  an  appreciable  effect  on  the  action,  and  back- 
flash  still  occurring  occasionally,  the  discharge  gas  coil  of  one- 
eighth  inch  copper  tube  shown  in  Fig.  I  was  removed  and  the 
square  coil  of  larger  iron  pipe  substituted  to  reduce  back  pressure. 
The  back  pressure  was  thus  made  constant  and  less  than  originally, 
and  the  charge  could  be  ignited  at  once  without  any  failure  with 
a  constancy  that 'was  very  gratifying. 


26  THE  HEAT  ENGINE  PROBLEM. 

Volume-ratios  During   Constant  Pressure   Combustion. 

When  the  fire  is  enclosed  and  insulated  the  immediate  effect 
of  constant  pressure  combustion  is  to  increase  the  volume  of  the 
gases  (  neglecting  the  small  changes  due  to  chemical  regrouping 
of  molecules).  Knowing  the  amount  of  heat  developed  by  the 
combustion  and  the  specific  heat  of  the  gases,  the  volume  increase 
should  be  easy  to  calculate.  But  in  such  a  calculation  no  account 
can  be  taken  of  the  large  number  of  other  influences,  among  them 
radiation,  conduction,  dissociation,  etc.,  involving  loss  of  heat 
to  other  phenomena  that  may  be  present  and  no  assurance  can 
be  held  out  that  the  specific  heat  during  the  process  is  constant 
or  equal  to  that  of  the  products  of  combustion.  A  computation, 
therefore,  by  this  the  only  method  is  of  no  value  in  engineering 
work,  and  the  only  way  to  obtain  a  result  of  real  worth  is  to 
measure  the  increase  directly  under  specified  conditions.  The 
method  used  has  already  been  noted.  The  firebox  consisted  of  a 
piece  of  six-inch  standard  steam  pipe  twelve  inches  long  and  the 
plates  containing  the  orifices  were  of  black  iron  one  thirty-second 
of  an  inch  in  thickness.  Unprotected,  i.  e.,  with  plates  bare  and 
pipe  unlined,  it  was  found  for  a  pressure  drop  of  four  inches  of 
Hg  through  each  orifice  that  the  maximum  effect  was  vjv±  =1.50 
for  best  mixture  air  and  gas.  Protecting  the  interior  of  the  com- 
bustion chamber  by  one  inch  of  fire  clay  and  sand  on  the  inside, 
the  lower  plate  carrying  a  clay  cone  three  inches  high,  and  the 
upper  plate  protected  externally  by  a  quarter  of  an  inch  of  asbestos 
sheets,  the  maximum  effect  was  found  to  be  vjv±  =  4.20  for 
best  mixture  air  and  gas.  Comparing  the  heating  value  of  the 
gas  used  with  that  of  say  kerosene  oil,  and  making  an  estimate  of 
losses  from  above  values  it  is  probable  that  with  the  best  mixture 
of  kerosene  and  air  that  a  value  z/2A'i  =  6.00  might  be  expected, 
but  it  must  be  remembered  that  this  is  only  an  estimate  and  of  but 
little  value  compared  with  the  last  two  figures  of  actual  ob- 
servations. 

The  apparatus  used  here  was  so  certain  in  operation  and  constant 
in  results  that  the  readings  could  be  obtained  in  a  very  short  time 
and,  when  obtained,  relied  upon.  The  method  of  operation  was 
as  follows:  The  fire  was  started  in  the  chamber  with  top  plate 
removed;  once  burning  steadily  this  plate  was  bolted  down  to 


CYCLIC    ANALYSIS    OF    HEAT  'ENGINES.  2J 

the  flange  and  the  whole  allowed  to  heat  up.  The  top  orifice  was 
originally  the  same  size  as  the  lower  and  as  the  fire  pot  heated 
up  was  continually  reamed  out  to  keep  the  manometer  readings 
at  the  ratio  of  2  :i,  i.  e.,  so  that  the  drop  in  pressure  was  the  same 
through  both  plates.  When  continued  heating  showed  no  in- 
crease in  size  of  the  top  hole  possible,  then  manipulation  of  the 
mixture  was  resorted  to  to  cause,  if  possible,  a  rise  in  pressure  in 
the  combustion  chamber  and  so  permit  a  further  enlargement  of 
the  upper  opening  to  bring  the  pressure  again  to  one  half  that 
existing  in  the  lower  chamber.  Thus  the  maximum  effect  was 
obtained.  It  must  be  remembered  that  the  readings  included  the 
friction  effect  of  passing  through  the  mass  of  broken  rock  forming 
the  burner  proper. 

Pressure-Ratios  for  Constant  Volume  Combustion. 

As  is  the  case  with  volume  ratios  in  constant  pressure  combustion 
it  is  impossible  to  calculate  the  values  desired  from  calorific 
value  and  specific  heat.  Many  determinations  of  the  presence  of 
ratios  for  various  substances  have  been  made  but  none  for  a  wide 
range  of  mixtures  including  as  one  of  the  constituents  neutral 
products  of  combustion. 

Each  mixture  of  air  to  gas  within  the  range  of  combustibility 
was  fired  and  then  to  each  was  added  in  turn  successively  increas- 


PlG.  XIII 


FIGS,  n,  12,  and  13. 

ing  amounts  of  neutral  gases  obtained  by  burning  an  explosive 
mixture  as  described. 

It  appeared  that  the  resulting  pressures  were  intimately  con- 
nected with  the  percentage  of  dilution  of  neutral  or  excess  gases, 


28 


THE    HEAT    ENGINE   PROBLEM. 


and  as  the  gas  used  has  already  exhibited  some  agreement  with 
what  is  possible  with  the  typical  water  gas  chosen  in  comparison  it 
will  be  well  to  work  out  a  table  of  percentage  of  dilution  of  dif- 
ferent mixtures  and  these  figures  will  be  placed  on  the  curves  of 
Figs.  11-16.  The  agreement  and  evident  existence  of  a  law  is 
apparent. 

.    WATER  GAS  OF  NOTED  COMPOSITION. 


Mixture 


f  Air,  3  1 
'    I  Gas,  I  } 


diluted. 


Gas. 

Air. 

Added   Neutral. 

Primary  Neutral. 

Total  Neutral. 

Per  cent.  Neutral. 

I 
I 
*     I 
I 

3 
3 

3 
3 

O 
I 

2 

3 

2.83 

« 
« 

2.83 
3.83 
4.83 
5-83 

70.1 
76.0 
80.5 
83.0 

Mixture, 


f  Air, 
(Gas, 


diluted. 


Gas. 

Air. 

Added  Neutral. 

Primary  Neutral. 

Total  Neutral. 

Per  cent.  Neutral. 

4 

0 

3-43 

3-43 

68.7 

4 

I 

« 

4-43 

74.0 

4 

2 

« 

5-43 

77.6 

4 

3 

« 

6.43 

80.6 

4 

4 

« 

7-43 

82.8 

f  Air, 

(Gas, 


diluted. 


Gas. 

Air. 

Added  Neutral. 

Primary  Neutral. 

Total  Neutral. 

Per  cent.  Neutral. 

5 

O 

4-05 

4-05 

67.5 

5 

I 

« 

5-05 

72.1 

5 

2 

« 

6.05 

75-7 

5 

3 

« 

7-05 

78.4 

5 

4 

« 

8.05 

80.5 

Mixture 


f  Air,   6  1 
'   I  Gas,  i  } 


diluted. 


Air. 

Gas. 

Added  Neutral. 

Primary  Neutral. 

Total  Neutral. 

Per  cent.  Neutral. 

6 
6 
6 
6 
6 
6 

0 
I 

2 

3 

4 
5 

4.96 

< 
« 

4-96 
5-96 
6.96 
7.96 
8.96 
9.96 

70.4 
74-4 
77-3 
79.6 

81.3 
84.0 

CYCLIC    ANALYSIS    OF     HEAT    ENGINES  . 


29 


Mixture,   {  ^  71   diluted 
{  Gas,  I  j 


Air 

Gas. 

Added  Neutral. 

Primary  Neutral. 

Total  Neutral. 

Per  cent.  Neutral. 

7 

0 

5.96 

5.96 

74.6 

7 

I 

« 

6.96 

77-3 

7 

2 

« 

7.96 

7#6 

7 

3 

u 

8.96 

8i-3 

7 

4 

« 

9.96 

83.0 

The  curves  of  Figs.  12-16  show  the  pressures  given  by  the 
indicator  for  each  mixture  and  are  the  mean  values  from  a  large 
number  of  lines  drawn  by  the  indicator.  These  curves  are  com- 
bined in  Fig.  17,  which  is,  therefore,  a  curve  of  pressures  for  all 


FIG.  xiv 


FIG.  xv 


FIGS.  14  and  15. 


mixtures  diluted  or  not  within  the  range  of  explosive  combusti- 
bility. The  numbers  on  the  curves  show  the  percentage  of  dilu- 
tion of  the  typical  water  gas.  The  results  are  most  remarkable 


30  THE    HEAT    ENGINE    PROBLEM. 

and  can  be  accounted  for  only  by  assuming  that  the  presence  of  a 
large  amount  of  dilution  hinders  combustion.  The  limits  at  which 
combustion  ceases  to  be  possible  on  too  great  a  dilution  are  here 
indicated,  whether  that  dilution  be  due  to  excess  gas,  excess  air 
or  neutral  gases.  It  will  also  be  observed  that  the  character  of  the 
diluenl  has  an  appreciable  effect,  but  that  when  the  dilution  is  least 
the  pressure  is  greatest,  about  60  pounds  above  atmosphere  or  a 
ratio  of  5 ;  and  the  presence  of  a  constant  per  cent,  of  neutral  will 
make  combustion  impossible  no  matter  what  the  mixture  of  air 
and  gas.  The  greatest  neutral  dilution  gives  the  least  pressure — 
about  15  pounds  above  atmosphere,  or  a  ratio  of  about  2.  These 
results  give  a  reason  for  the  decreased  pressure  in  exploding  gas- 
engines  in  which  the  mixture  is  always  diluted  by  burnt  products 
.to  an  extent  of  20-40  per  cent,  of  the  volume  of  neutral  addition 
to  the  gas  mixture  which  may  already  have  neutral  gas  present 
to  the  extent  of  65-70  per  cent. 

Neutral  additions  to  the  gases  sent  to  the  calorimeter  and  to 
the  other  apparatus  showed,  besides  a  corresponding  and  proper 
heat  value  for  the  resulting  mixture,  a  decreased  rate  of  propaga- 
tion accompanied  by  a  difficulty  in  ignition  and  constant  tendency 
to  incomplete  combustion,  i.  e.}  tendency  to  cease  burning  after 
inflammation  had  been  started  and  before  the  mass  had  been- 
entirely  burnt. 

CONCLUSION. 

The  next  step  in  this  work,  now  that  the  mathematical  dis- 
cussion and  determination  of  the  physical  action  and  constants  is 
finished,  is  naturally  to  apply  the  results  to  an  operating  machine. 
It  seems  that  the  best  arrangement  would  result  in  the  combina- 
tion of  a  compressor,  a  fire  chamber  and  gas-expansion  turbine,, 
and  it  is  the  construction  and  test  of  such  a  combination  that 
will  form  the  subject  of  the  next  work.  However,  as  this  point 
marks  a  natural  division  of  the  subject  and  as  sufficient  has  been 
developed  to  more  than  fill  the  requirements  of  a  doctor's  disserta- 
tion, the  remainder  of  the  work  will  be  left  till  later,  though  it  is 
with  sincere  regret  that  this  investigation,  already  so  fascinating 
and  so  fruitful,  is  even  temporarily  laid  aside. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


LD  21-100m-7,'33 


